What to do if the city failed to board up an abandoned house and my home next door was destroyed as a result?

The city may have an administrative claims procedure that you may need to follow prior to filing your lawsuit against the city.  If there is a mandatory administrative claims procedure, don't miss any filing deadlines or you might not be able to proceed with a lawsuit after the administrative claim is denied.  Administrative claims against a city are usually denied.

Your lawsuit against the city would be for negligence; however, there may be some problems in proving negligence on the part of the city.  Negligence is the failure to exercise due care (that degree of care that in this case a reasonable city would have exercised under the same or similar circumstances to prevent foreseeable harm).

In order to prove negligence, you will need to prove duty (of due care) mentioned above, breach of duty (failure to exercise due care), actual cause, proximate cause and damages.

Actual cause means but for the city not boarding up the abandoned house, would your house have been destroyed in the fire?  If the answer is no, actual cause has been established.  The problem here is that even if the city had boarded up the house, the flames still would have spread to your house.  So, it may be difficult to prove actual cause.

Proximate cause means were there any unforeseeable, intervenng acts which would relieve the city of liability?  If the answer is no, proximate cause has been established.  It may be difficult to prove proximate cause because the city could claim that the arsonist burning the abandoned house was an unforeseeable, intervening act which would relieve the city of liability.

If you do prevail in the negligence case, your damages (compensation you are seeking in your lawsuit for negligence), would be the loss of your house and its contents.