As long as you have liability insurance you should be alright, and unless the property was not properly maintained or you did something negligent it should not be an issue. You cannot deny her application or evict her due to her age so why worry about something beyond your control. Depending on the laws in Florida if she did pass away in the home you may have to disclose that if you ever intend to sell the home.
I use a form that give authorization to allow access to unit/personal property. This form basically states that in the event that the resident becomes incapacitated or dies that they will grant access to their unit and personal belongings and will hold you harmless. If you do not have this type of form already I would recommend you get one on hand for any properties with aging tenants. It helps in the event that they do pass. Everything seems to happen so quickly and most people do not have a will set up. Family members start to pressure to gain access to things some who have good intentions and others who do not. This way this gets the landlords off the hook and also can help the transition be a lot more smooth. Also I would look up the disclosure laws in your state because in California you are required to tell any applicant for that up that a death had occurred there for the next 3 years. Regarding insurance as long as there is not anything that is a safety or trip hazard that is due to your negligence then I would not be concerned. However consulting with an attorney and your insurance agent would not hurt. Just to make sure you are properly covered in the event that something did occur. I would definitely make sure the house is under an LLC.
Don’t worry about her passing as long as you have maintained the home. Make sure on your application that you have the person to contact in case of an emergency. In Florida, you do not have to disclose if someone dies, killed etc.... although I think it is better to do so instead of finding out from the neighbor!!
The one big issue is when people try and come and remove belongings out of the house, and you let them, you could be held liable. You must make sure you have legal documentation about who can remove those items
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