Yes, I have played this variant before. This was a common game my family played when I was a kid, and we still play it now and then. We had slightly different rules about the king- it was just a normal piece for us, that could be captured and capture just like any other piece. I think that helped to balance the game somewhat, and was a slightly more equal variant than what you have described.
Wikipedia also describes this variant. It has many names, the ones I have seen most commonly are Takeaway Chess and Antichess. It is described on Wikipedia with the same version of the rules I have described (https://en.wikipedia.org/wiki/Losing_chess), and a bit of the game's history and strategies. Wikipedia also claims that it has been weakly solved as winning for white with 1. e3. Thus, it has been proven that white always wins, but every line has not been calculated for the forced win (if this makes no sense, you can read about the different ways games can be solved here). However, since no one can memorize the number of potential lines required to win it, you can still play it and be competitive in your games with your friend.
Furthermore, Wikipedia provides several other lists of rulesets for this variant that are less common but still played in some local areas. Yours is one of them, so I would assume that your friend got this from an area where that version of the variant was played.
I have seen Antichess on chess.com, on the 4 player chess server. It is not currently among their standard 2-player-chess variants, perhaps because it has indeed been solved and wackos who wanted to get crazy ratings would be able to use computer help much more easily, or just memorize a bunch of winning lines. I agree with their evaluation of there not being much use of putting it in the 2PC variants, but the 4PC variant is quite fun, and has not been solved as an extra bonus. :)
It occurred to me after writing the above paragraph that Lichess has this among their 2PC variants- in fact, I checked and it is apparently their most popular variant- even more than Chess960. So I guess it can work in 2PC online. I'm pretty sure that while it's not recognized by FIDE or anything, being on Lichess and chess.com indicates that it is a major part of the chess community. Many other variants, like Chess960 have gained steam in local clubs, online, and in mid-level tournaments, before getting recognized as a real thing by FIDE. I don't think that will happen with Takeaway Chess, since it's already solved, but it still seems to have a sizeable community.
As for strategies as Black, you can read the Wikipedia article I already cited for deeper analysis and other references, but I'll summarize some stuff here.:
As black, the variation that is the hardest to play against as white is the
Liardet Defense, which is
1. e3 b6. This makes the game take a very long time, and can send the game into an endgame, which are much more ferociously complicated than normal chess endgames, and can for all practical purposes make the game a coin toss when the game is played between two not-Magnus-Carlsen-level players. Thus, I would suggest that you try to figure out how to get into an endgame, which should actually be far more complicated than the middlegame, where there are more pieces on the board, counterintuitive though it may seem.