If you are risk adverse real estate, (especially out of state) is not for you.

I am not sure if her health condition is purely physical or if it's adversely affecting her mental faculties, but if you have a strong relationship and rapport you can have a candid and open conversation about your intentions and demonstrate any way you can help (through deeds, financial support, etc). 

If a person squats long enough to claim adverse possession there could be a problem, but that person would have to reside in and care for the home for 10 years and pay the taxes on the property during that time.

@Kyle MarekYour grandpa will likely be adverse to OOS.

Mine says, in part:CRIME-FREE / DRUG-FREE:You, a guest or other person under your control shall not engage in illegal activity on the Premises or near enough to adversely affect it or other residents.This includes:...c.

Another factor is the statute of limitations on the TN tax sale, and colaterally the statute of limitations on adverse possession. 

unpermitted work is an adverse condition, and legally you must disclose it.Once you disclose it and the house is sold, if the county has an issue, is up to the new owners to deal with it.  

Depends on how risk adverse you are. the City of East Cleveland (different entity from the City of Cleveland) went bankrupt decades ago, and unless things have changed since I moved south, shows no signs of ever recovering.

Update: I spoke with my mortgage company to make sure there would be no adverse consequences to having the lots taxed separately from each other.

. § 1923.04 A party desiring to commence an action under this chapter shall notify the adverse party to leave the premises, for the possession of which the action is about to be brought, three or more days before beginning the action, by certified mail, return receipt requested, or by handing a written copy of the notice to the defendant in person, or by leaving it at the defendant's usual place of abode or at the premises from which the defendant is sought to be evicted.Emphasis mine.That is for evictions.