Zero. You do not own the property. You have zero rights to the home or anything inside.
You might.... might be able to ask that the city condemn the house and find the home to be a public nuisance and board the thing up. A more seasoned property attorney may know better than I.
I'll re-post this to the property list.
Matthew Johnson phone# 206.747.0313 is licensed in the State of Washington and performs bankruptcy, short sale negotiations, and estate planning in Whatcom, Skagit, Snohomish, King and Pierce counties. The response does not constitute specific legal advice, which would require a full inquiry by the attorney into the complete background of the facts and circumstances surrounding this matter; rather, it is intended to be general legal information based on the limited information provided by the inquirer; it This response also does not constitute the establishment of an attorney-client relationship, which can only be established after a conflict of interest evaluation is completed, your case is accepted, and a fee agreement is signed. Johnson Legal Group, PLLC
Mr. Johnston is entirely correct, under "default" real estate and civil law principles , you would be trespassers on this property and have no rights to even enter on it, much less improve it.
That being said, I agree with counsel that you might want to talk to the municipality and have the property condemned (in which case the owner and former resident might be compelled to repair the property, or fence it off, board it up or similar steps if it is dangerous, a public nuisance, or violated municipal requirements to keep property repaired and in good order to protect neighborhood character and property values,
Another tack might be to contact the owners of the property and get written permission to enter the property and effect basic repairs, like boarding up the doors and windows, mowing the lawns and similar cosmetic or safety improvements. You can find out who owns the property where deeds and real property records are located, in some places, even online. Is the property abandoned or in foreclosure? The bank or municipality who holds the title might be very interested in the neighbors making improvements that would keep the property from further deterioration and perhaps even make it saleable,
The key, though, is do your homework, ascertain the owner, and ask first before resorting to self-help.