Basically what the title says. I've only played two games like this so far (Silent Hill 2 and OMORI) and am looking for more.
Could be games, ROM hacks, mods of existing games, etc.
EDIT: So many great suggestions! Getting a bit overwhelmed by how many there are, so I'm going to need to find a way to put this in some kind of list with an order to play the games in. By all means, keep 'em coming, though!
Have you played Plague Tale 1 and 2? I'm not considered a very emotional person, but the dynamic really got to me. Just a really solid game, enjoyable combat. They're two of the very few games I binged to completion.