I've tried using the lingering wounds, and found it to be an absolute disaster. If you plan to use them, expect high PC turnover rate, since it takes either a lot of downtime or powerful magic to recover. Even in a gritty game, I'd probably only have them happen on a rare occasion, such as @Doc_Klueless suggested with a Critical Hit that reduces you to 0 HP. I don't like adding them from a failed death save, because to me that's adding the injury retroactively (the narrative has already determined your fall).
If I was going to use it again, I'd have a check happen every time you drop to 0 HP. Perhaps a 1 in 20 or 1 in 100 each time (depending on how vicious you want it to be), then a roll on the lingering injuries table. This would also completely eliminate the problem some have with a character going down each round, only to get back up each turn, before getting knocked back down. Using this, anyone dropped to 0 HP and healed is likely to play dead or withdraw from combat until healed more.
If I was going to use it again, I'd have a check happen every time you drop to 0 HP. Perhaps a 1 in 20 or 1 in 100 each time (depending on how vicious you want it to be), then a roll on the lingering injuries table. This would also completely eliminate the problem some have with a character going down each round, only to get back up each turn, before getting knocked back down. Using this, anyone dropped to 0 HP and healed is likely to play dead or withdraw from combat until healed more.