what if an older tenant dies in my house?

[Everitt Gill]

I'm looking to buy a property as a buy and hold rental unit, the numbers look good but there is one big potential problem. the current tenant is 80 years old. what happens if she dies in there? should I be concerned with legal problems if she falls in the house and then her family sues me? do I need to buy some sort of special insurance or anything for this? I'm very ignorant when it comes to this, any help would be appreciated. the property is in Florida