What do you mean by "lag switches" -- are they simply disconnecting during their game, or do you mean that the amount of clock correct for lag increases when your opponent is in a losing position and that you suspect them of somehow deliberately introducing communications latency to gain more time to think? The game you've posted ends in checkmate, so I'm unclear what you mean by "internet connection is broken" since if this were the case, checkmate could not have been the outcome.
I'm not a sore loser, but...

What do you mean by "lag switches" -- are they simply disconnecting during their game, or do you mean that the amount of clock correct for lag increases when your opponent is in a losing position and that you suspect them of somehow deliberately introducing communications latency to gain more time to think? The game you've posted ends in checkmate, so I'm unclear what you mean by "internet connection is broken" since if this were the case, checkmate could not have been the outcome.
I have encountered those suspicious instances, too, where my opponent's time seems not to decrease. The game I posted actually ended after my 16th move; I only posted the continuation that would have happened if my opponent did not 'lose connection'.

It seems to me that a lag switch would only hurt your opponent by making him unable to move for the lag period. Unlike online video games, your opponent can't continue to play chess at Chess.com while he is disconnected from the server.
A lag switch would help someone gain a few more seconds to study the position without losing any of his or her time. That's similar to what happens in video games where the lag switch would be used to reposition something at an opportune moment while the opponent is unable to respond due to the loss of connection.

What is a "lag switch"?
A lag switch, according to my son, is a device that temporarily suspends internet connections. They are often used by cheaters during online action games.

I see.
If they simply disconnect you still get the win (and they get the loss) so there's no real incentive for them to do so.
Sometimes an opponent will walk away from a game, leaving you to babysit a game in which their clock is simply counting down to their inevitible time out. Sometimes these players come back and sneak in a move in the hopes that you've also walked away and that it will then be you that times out. Although you can't say for certain whether they were legitimately using their time to think or not, in many cases it's quite obvious what their trying to pull. These are the players most deserving of a block.
I seriously doubt that anyone deliberately introduces latency into their connection to gain some kind of advantage. Even if it were technically feasibly, I'm not sure it could be done in such a way as to confer an advantage (i.e. if done during their turn it doesn't result in any additional time for them and if done during yours they don't see your move until the extra time is used up and then it's their turn again). I can see how this could work in real time gaming to cause deliberate slow downs (for which you are prepared, but your opponent is not), but I just don't see how it could work for a turn based game like chess. I really don't think you need to worry about this as a legitimate possibility. Lag happens for legitimate reasons and the corrections are by design and are just that -- corrections.

Again, though, if the player does it while it's their turn their clock doesn't stop counting down. If the player does it while it's their opponent's turn they don't see their opponent's move until it's made, at which point their clock starts counting down again. I just can't see how it could confer the same advantage in a turn based context.
Also, remember that both players get the extra time since the lag is corrected in both directions for the aggregate latency.

I instantly block people like that. It's dead obvious they are doing something. And if they are not, tough luck; get a better connection.

Come on, how much time could they really gain? This is chess, not a multiplayer shooter game where a second here or there can make a huge difference.
Except perhaps in bullet chess.

Sometimes an opponent will walk away from a game, leaving you to babysit a game in which their clock is simply counting down to their inevitible time out. Sometimes these players come back and sneak in a move in the hopes that you've also walked away and that it will then be you that times out. Although you can't say for certain whether they were legitimately using their time to think or not, in many cases it's quite obvious what their trying to pull. These are the players most deserving of a block.
Ugh, I get this constantly. My blocked list is filled with these people.

Sometimes an opponent will walk away from a game, leaving you to babysit a game in which their clock is simply counting down to their inevitible time out. Sometimes these players come back and sneak in a move in the hopes that you've also walked away and that it will then be you that times out. Although you can't say for certain whether they were legitimately using their time to think or not, in many cases it's quite obvious what their trying to pull. These are the players most deserving of a block.
Ugh, I get this constantly. My blocked list is filled with these people.
I always get a strange satisfaction from blocking this kind of person.

And Grobe, I've never seen my clock run backwards like that - not during the game or after I've timed out. So how could you say the adjustments affect both clocks, have you ever seen your clock run backwards in the same fashion?
You will never see your time corrected, only your opponents. Rest assured, though that your opponent sees the corrections applied to your clock. Here's why:
Once you've made your move your opponent's clock starts counting down on your computer. The notification goes from your machine, to the chess.com server, to his (incurring lag) at which point his clock starts counting down on his machine. Once he's made his move the notification has to go from his machine to the chess.com server to you (incurring lag yet again) at which point your record of his clock is corrected for the total lag recorded during the above events.
Now let's look at this from your opponent's perspective:
Once you've made your move your opponent's record of your clock hasn't yet stopped counting down on his computer. The notification goes from your machine, to the chess.com server, to his (incurring lag) at which point his record of your clock corrects for the lag incurred (plus the lag from when he sent you his previous move). Once he's made his move his record of your clock starts counting down immediately while the notification has to go from his machine to the chess.com server to you (incurring lag yet again) -- lag that will be tacked back onto his record of yourclock, along with the additional lag incurred during the transmission of your next move once he receives that.
You will neversee your own clock corrected, however the amount of correction you see on your opponent's clock will always be equal to the amount of correction your opponent sees on yours. It's a zero sum game, and there's nowhere in that sequence that I can find where deliberately introducing lag could confer an advantage.

Sorry, but I'm just not buying it. Sometimes lag is actually lag. Actually, I think lag is simply lag on this server. Erik says that it's buggy code, why not take the owner's word for it? I simply can't see many people having, let alone using, let alone benefiting from the use of a lag switch. Not credible.
What he said, only much less concise.

I've suggested in the cheating forum, where you and I are both participating in a similar discussion, a number of legitimate ways in which significant lag could be realized.
When you play the computer, only your portion of the latency (there and back) and any chess.com server delay will contribute to latency. This is actually a good indicator that when you see lag it tends to be in your opponent's connection (which you seem to be implying) and not in yours (which agrees with what you've also suggested) or the chess.com server load, however, which you have implicated.
Given this, I'm curious to know where you think in the process I've outlined deliberately introducing lag would confer some kind of advantage. Perhaps I'm just not seeing it, or there's an exploitable bug I'm not aware of in the lag adjustment algorithm, but I don't think that it's there.

This has happened to me once while I was playing 1 minute bullet chess. My opponent's clock kept bouncing back up to a few seconds each time it hit zero, in other words, he somehow couldn't lose on time. I only had 14 seconds and I ended up losing on time. My opponent was just taking his time.

Here we go again! I just finished playing someone in a 4 minute blitz match. My opponent's rating was 1769 (his rating is 2100+ in correspondence...hmmm), which is pretty good. We're moving blow for blow with no connection problems. I noticed during the first 8 moves of the game that my opponent had a little lag on his time, not much. Suddenly, after my 9th move, he lost connection. There was 3:31 left on my clock, while his was just dwindling down until his clock reached 0:19.4. That's when it was determined that he 'abandoned' the match. Coincidence? Could be, be here's what I believe happened.
I'm aware that when using a lag switch the user runs the risk of lagging too long, and connection cannot be re-established. The position of our game after move 9 was a little tricky, so I think that he wanted a few seconds to study the position. He hit the switch, but did not re-connect in time. I could be wrong, but I doubt it.
...I have suspected for a long time that many players use lag switches during blitz games. Admittedly, I don't have any proof, but the following sequence happens SO often that doesn't seem coincidental: I and my opponent are moving blow for blow and second for second. Suddenly, when the position is losing for my opponent (or the position is a little complicated) internet connection is broken. Pardon my venting; I normally just block the suspicious player. I'm wondering does anyone else encounter a similar sequence of events during blitz games. Is there anything else that could be done?
This is an actual game where I suspect my opponent used a lag switch. I won't use real names since, as I said before, I have no proof: