[Help] Need advice regarding legality of giving a dog away when she still has a different owner

I live in Oakland, California. My upstairs neighbor has a serious drinking problem and as of about Tuesday of last week just left his dog in the yard for two days. Eventually we let her into our apartment and gave her food and water. There's four of us living in our apartment and all of us have knocked on this guy's door trying to get him to let his dog back in but he won't open the door or acknowledge her. He's definitely home. In fact, I don't think he's left his place for a week. I left texts and a voicemail but no answer. We're looking at adoption possibilities for the dog. Problem is, she's an old dog. Sweet natured and fine with other animals but around fifteen with bad hips. There are senior dog adoption centers that could possibly take her but there's the issue of ownership since she doest technically still have an owner. One place said they would send me a basic template of surrendering dog ownership that we could try to get the owner to sign so that we get ownership and then can find a place for the dog.

Given our neighbor's history over the past year, I seriously doubt he is ever going to get sober. He almost died from it last year, his friends put him in rehab, but he came back early and immediately started drinking again. He's literally left pools of blood twice on the concrete steps leading up to his apartment from falling down and bashing his head. He wouldn't accept help, we had to clean the blood up, and he still keeps drinking every day all day. So I don't see him being fit anytime soon to look after his dog.

What happens if our neighbor won't sign this paper and still won't take his dog back? Is there a point in time by which it can be considered abandonment and he has legally surrendered ownership? Could he sue us for giving his dog away if we did so without a signature from him?

Edit: thanks for the responses, everyone! I will call animal control soon and see what they say before we make a move with the dog. As for the neighbor we do see his lights go on and off and hear him moving around from time to time so we know he’s not dead yet but if that stops we’ll call the cops to check on him