Yes, it is this variation M. pfren.
Though, I don't understand : "analysed to death" ?
Development in a specific line of the 4... Bf5 Caro-Kann
After 13. Ne4 Nxd4 14.Qd4 Nf6 15.Qe2 Qd5 16. Kb1 Qe4 is fine for black. White can play 15. Qd3 to mix it up a bit, then the Qd5 plan isn't so good as the other guy pointed out. After 13. Kb1 theres a lot of ideas to avoid getting mated by playing some usefulish waiting moves like Qc7 to see what white does since g4 doesn't do much if the kings still on e8. You can play O-O which is probably the main line but you run the risk of getting mated, especially if you don't know the theory.
M. Spinaltap, could you tell me where I can find the 0-0 theory (analysed in depth) ? (books, videos, ...)

Yes, it is this variation M. pfren.
Though, I don't understand : "analysed to death" ?
It means that a serious player should avoid that variation at all costs, with either color: there is always some danger drawing against a patzer which is just parroting opening moves.
M. pfren, do you mean that, as Black, I should avoid playing this ? But what if my opponent is going for this variation ? Do you mean that I should study an other variation (such as 4... Nd7) or an other opening ?

M. pfren, do you mean that, as Black, I should avoid playing this ? But what if my opponent is going for this variation ? Do you mean that I should study an other variation (such as 4... Nd7) or an other opening ?
You can keep chances alive with 17...f5!? (instead of 17...Nxf2)

There is also 15...Ng4, 15...Qb6 and 15...b5 (instead of 15...0-0). All three of them look quite playable.

I recently had a game where I castled queenside as black.
I did pretty well in the game, I wonder if this is playable?
Isn't queenside castling a bit passive for Black ? (I mean better prospects for White)
What do you prefer between kingside and queenside castling M. pfren ?
Mainline_Novelty : did you find your preparation ? Would you agree to share it ?
I have an other question for everybody : after 15. Qe2 Qd5 16. Kb1 Qe4, what is best play for Black if White does not take the queen but instead plays a rook on e1 or Be3 ?
And if Queens are traded on move 17, how does Black to reduce as much as possible white knight's activity ?
I'd like to thank you all for answering and exchanging ideas, that's very great.

After 13. Ne4 Nxd4 14.Qd4 Nf6 15.Qe2 Qd5 16. Kb1 Qe4 is fine for black. White can play 15. Qd3 to mix it up a bit, then the Qd5 plan isn't so good as the other guy pointed out. After 13. Kb1 theres a lot of ideas to avoid getting mated by playing some usefulish waiting moves like Qc7 to see what white does since g4 doesn't do much if the kings still on e8. You can play O-O which is probably the main line but you run the risk of getting mated, especially if you don't know the theory.
M. Spinaltap, could you tell me where I can find the 0-0 theory (analysed in depth) ? (books, videos, ...)
Not sure where you could find that for free. There's always chessbase which is very expensive. It might be in the lars schandorff caro kann book, but I'm not 100% sure haven't opened it up in awhile. I wouldn't worry about it though at your level. Your opponents aren't going to get that far anyway.

Schandorff in his book dismisses the lines with long castling for Black as dull, and suggests plans with short castling- factly, only 15...0-0 is examined.
Thanks M. pfren for your deep analysis (comment 24), I came to a conclusion : classical variation (4... Bf5) is OK, and after 16. g4 Nxg4, Black has 2 interesting moves : Nxf2 (which seems to lead to draw with precise play) and f5 (with chances for both sides).

Ummm, hardly an analysis. Just a collection of mid- to-hi level games played in that variation, which IMO is already archived as a draw.
I have an other question for everybody : after 15. Qe2 Qd5 16. Kb1 Qe4, what is best play for Black if White does not take the queen but instead plays a rook on e1 or Be3 ?
And if Queens are traded on move 17, how does Black to reduce as much as possible white knight's activity ?
Do you have some answers for those 2 questions please ?
In fact, 16. Kb1 could be a mistake for White, cause Black can then play Nxh5, though after 17. g4 Nf6 18.g5 Ne4 19. gxh6 Rxh6, Black should castle queenside.
Thus, we can assume that White will, in all likelihood, play 16.c4 and after 16... Qe4, if 17. Be3 (in order to avoid the exchange of queens), we can play 17... b5, attaquing on the queenside, moreover, black queen is very active.
Back to my experience: When I played this line 30 years ago it appeared very solid to me. The problem for black is unbalancing this. So you need a backup for cases you have to play for a win with black.
By "backup", you are talking about other openings in the repertoire, so, what's your advice ?
For example, in my club, somebody knows very well this 4. Bf5 line. In order to win against those opponents (not only playing for a draw), I have to learn other openings, but highly sharp theoretical one-move-blunder openings cut both ways so, I prefer more "solid" openings. How about the 4. Nd7 Caro-Kann ?
In fact, Caro-Kann has the advantage to be both solid and acheving equality. Other openings don't : 1. e4 e5 is passive for Black ; 1. e4 c5 cut both ways, as I said ; and 1. e4 e6 has an annoying drawback : the light-squared bishop is trapped in our pawn structure.
Isn't this particular variation been analysed to death (and a draw)?