What if your tenant claims that his belongings were stolen when the exterminators were at the house?  

Never had stuff stolen from the site.However, once I started showing a house I did have the copper pipe stolen from the crawl space.  

I require a gov't issued photo ID to verify that the applicant's identity isn't stolen or fake; a copy of this is kept in the application file.

Have you done any research to make sure your identity wasn't also stolen by this tenant?

I've had a fair number of ads stolen and so longer post on craigslist. 

Companies/Users got hacked and their coins stolen, the records  ladger containing the data was never hacked. 

We also take out the window units so they don't get stolen and we screw the crawl spaces shut to discourage copper thieves.

condenser units stolen like crazy  etc etc.. then they just give up and walk away and get blamed by the very neighbors who did not take the time to help watch their property or it was their cousin that came over and stole everything when the tenant left.. 

I had a lot of my copper pipes stolen last night out of one of my properties.

Over the week end we opened a Lowes credit car and purchased $6,000 worth of merchandise.