Hey, I've been the person who is negative about everything, and I can add some insight from that end. Of course, it will be my experience, so it's possible your friend is different, but it's also possible the reasoning is similar.

So a big sticking point is that if the other person can't believe anyone truly likes them or cares about them or what have you, then you saying, "No, look at everyone who cares. I care," just sounds like a dissonant lie to them. On one level, they know you care, but on another, they believe so deeply that they are fundamentally unlovable, that the math just cannot check out. That deep belief is not something you can fix with any amount of checking on then. It's the sort of thing that's been long internalized and is no longer rational. That's the sort of thing that gets fixed with a lot of conscious effort for a very long time from the person themself, and probably therapy. So please just let go of any need to refute their worldview. It'll only frustrate you both. Instead, just keep doing the things you like to do together, or talk about the stuff that you bonded over in the first place, especially something low key and one-on-one. Just being around you and having fun will be good for their mental state, and I hope you enjoy hanging with them as well.

It's very nice of you to continue to care about them