Reason #1- Reduction of Liability
What if someone get injured while visiting your uninsured tenant? You would end up being liable. You could lose quite a bit of money by paying for a claim made with respect to injury, which can also cause your homeowner’s insurance premiums to rise significantly.
Reason #2 - Payment of Accommodations
You don’t have to worry about what living arrangements insured tenants will need to make if the apartment is unlivable, due to a covered claim, during repairs (that you are already paying for), and who will cover the cost.
Reason #3 - Coverage for Personal Property
While you are responsible for repairing damage to the dwelling, you cannot and do not cover the belongings of your uninsured tenants.
Chances are if anything was to happen, your uninsured tenant would come after you to recover financial losses. Renter’s insurance will give you peace of mind that should something happen, you do not have to deal with the renter’s losses and can concentrate on your own property and liability.
I recommend talking to your tenant today, for your protection and theirs. It's very inexpensive, and easy for your tenant to obtain a policy; a typical policy covering up to $15,000 in property damage and $100,000 in liability coverage costs about $100 per year.