It depends on the rating difference and the level of play. If, for instance, a player rated 1300 is playing a 1600 rating and somehow the 1600 player blundered a piece, then it may be appriate to play on. This is especially true if the higher rated player is in a good position and the lower rated player is making weak moves. However, a 1600 player is down a piece against a 2300 player then it would be outrageous to offer a draw. I had a 1350 player offer a draw when I was 2 queens up and it was mate in about 6 moves. That is just stupid and insulting. Most of the time the innappropriate offerers I experience are not mate next move but 3 - 10 points down and/or they are in time trouble. I find it strange that occasionally someone will resign after their first move and more rare is the player who offers a draw after 1 or 2 moves.
Most outrageous draw offers

Maybe this old Monty Python scene
- somewhat chess-related ...
The black knight, guarding a bridge :
https://www.youtube.com/watch?v=dhRUe-gz690
-" ok, we call it a draw .."

Lol so many online chess games are like this scene :p
No resignation and then irrelevant draw proposal!

After a long, stressful and difficult battle some people sense of decency collapse.
I agree. People on this site have a massive ego problem, and never seem to offer a draw at the appropriate time. Its always when you are winning, and they think you are stupid enough to accept.
Also, no-one wants to accept a draw either, even when the position is clearly drawn.
It's so irritating, and makes playing chess on here not fun sometimes.
After a long, stressful and difficult battle some people sense of decency collapse.
You can post here the most hilarious and absurd proposals you've got
Here is an example from a game I played on another site:
In this very position it is black's turn. White offers a draw: