There is available through some insurance companies and in certain areas, "Pet Damage" insurance. It's very limited and such pet damage coverage may only offer up to $500 in liability coverage in the event of pet damage to the rental property. This applies after any pet deposit and/or security deposit has been exhausted.
And yes there is a better way to handle the issue of when renting to applicants or tenants with pets.
What are the other options. Please provide, I need something to cover this issue and protect myself. 68% of tenants have pets. God only knows why renters who work all day and leave the poor animal along for 11-12 hours is just pain abuse. Thanks for any suggestions.