I Thank goodness for Landlords Insurance, however in order to make a successful claim you need a current address for the tenant (this is also needed to have a judgement recorded against them). :
I have had a tenant do a runner and have been able to claim the costs back from my insurer. (unpaid rent, letting fees, cleaning costs etc). I did not need to provide a current address for the tenant.
Would different insurers have different policies on this?
Regards Jason.