If you live in a town or city (vs. a more rural setting), call animal control. They will knock on the door and talk to the neighbor and/or cite him as violating town ordinance. Where I am, animal control will remove the cats if you catch them. We had one on our back porch during a terrible ice storm, no one knew where he came from (although my next door neighbor felt sorry for him and was giving him tuna...grrr!)I had to catch him, keep him in a pet carrier until animal control came by to get him.
Ours are SEIU members.
You're neighbor goes to heaven....guess where you're going.