What do you think I should do when my ex just randomly reaches out to me? I kind of want to reply.
Well, I'm not sure. Why do you want to reply?
I'm thinking I want them back, but I think it's morally wrong to get back with an ex who doesn't even deserve you.
No, that isn't morally wrong. Depending on why you broke up, it might not be wise. It isn't morally wrong in itself, though.
I want to give my ex another chance, because I believe their change will be permanent and stable and that they can put the past behind us.
Well, great! If your choice is to go back to them and you're going in with a clear mind, I don't think there's anything wrong with that.