Upstairs tenant overflowed tub, insurance won't pay

[Phillip S.]

This has happened twice now in a span of less than 6 months.  The property is a duplex with a tenant living in the upstairs unit and the downstairs unit is presently vacant.  The upstairs tenant overflowed the tub (again) causing water damage to the downstairs unit.  It wasn't serious, but it still cost me nearly $700 to clean up with water and have the ceiling in the downstairs unit repaired / repainted.  Luckily there was nobody living in the downstairs unit at the time or else their contents could have been damaged.

After contacting my insurance company I was basically told that damages caused by the tenant's actions are not covered, and my only recourse would be against the tenant or the tenant's renter's insurance.  Problem is the tenant has no renter's insurance and is on a fixed income with little or no ability to pay for the damages (she's elderly and Section 8).  So what in the world do I do here?