Ask the heir what kind of health care the decedent had.

Obviously you'd want to do a real in depth inspection of the property, and make sure that the property isnt so out of touch with code, health, and just overall standards of living.  

Unless someone in the house will have their health seriously affected (maybe asthma?  

You should also require this information is updated annually.You can still place reasonable restrictions on the animal, such as: Requiring a current (and annually updated) Veterinarian report on the health of the animal, including vaccine status; current appropriate local licensing of the animal if required in your jurisdiction; require the animal be spayed or neutered unless contraindicated by the Veterinarian; require the animal to be in a carrier or on a leash when in common areas of Multi-Family properties, particularly elevators or hallways and stairwells; require tenants to clean up after the animal in common areas and/or within their unit, and prevent offensive odors from emanating from their unit; aggressive or nuisance animals (includes frequent barking that is NOT an alert by the animal) can be cause for removal of the animal and/or eviction of the tenants.

Largely they are a disappointing extension of our already problematic health care system.

We have a typical comprehensive health care insurance plan, through my employer that covers both of us.

Someone with the avoidance issues you describe probably has some mental health issues.

I currently have a comfortable job making about $60K a year and have decent health insurance, but it is not related to real estate in any way.

I come from a mental health background and my knowledge of real-estate investing is limited to owning my own home.  

He can do anything for you on flood/auto/home/rentals/life/health, he is who I go through with all of my stuff so I can personally vouch for him.