How to deal with an abandoned home
Call your local government
If the issue is a safety hazard — like tree limbs leaning on power lines or a walkway that hasn't been shoveled after multiple snowstorms — your city or town might be able to help. Public works departments can take care of these potentially hazardous situations (or ones that are not so hazardous, like unmowed lawns), and then charge the homeowner for their services, either through tickets or fines.
Whether or not that will make a difference depends on the homeowner. A lien put on a property for unpaid maintenance costs could spur an owner into action, though most likely not if there's already a lien there for unpaid property taxes. It's worth a shot, though.
Also, getting the home on the city's radar is a good idea in case squatters try to move in, or thieves start to take away whatever they can get their hands on, like copper pipes.