I'm wondering if a pet-sitter steals our pet, what happens?

I think you should call Rover directly and ask them. I assume you own a very expensive pure bred show dog worth over $10K, and it's understandable you are worried that a regular pet sitter may want to steal your show dog. I have no idea if Rover will compensate you for the price your dog is worth right now (maybe after being a state champion or something) or if they would pay you the price you paid when purchasing your pup and have a bill of sale. But please do share with us regular sitters what Rover told you after you explained them your situation? I am very curious too.

On the other hand, most of us sitters are not thieves or criminals waiting to rob you the second you give us access to your house. We all want clients to be happy and come back to us. But you should definitely get your sitter vetted by a 3rd party if you this is a situation that's not common, and have cameras set up, plus get a copy of her ID and write a separate contract. I personally have never heard of a Rover sitter stealing a pet from her clients. Good luck with your search.

Rover staff may direct you to the Terms Of Service. Sections 2 & 16. https://www.rover.com/terms/tos/

If any exceptions are made, that would be authorized through Rover staff, so you’d need to contact them directly, as Lenka advised.