Do rental cars get stolen and if so do the rental companies have theft insurance?

Unfortunately - yes, rental cars do get stolen. Most rental comapnies have theft insurance, but usually have some sort of deductible. Rental cars get stolen from customers all the time. If you were to accept the Lost Damage Waiver from most companies, the car would be covered, there is NO deductible. Now if you were to leave the keys in the car, or give them to someone and they took off with the car; you are out of luck.

This is correct. LDW/CDW (depends on the state) would cover the car as long as the contract was not violated and as long as it wasn't stolen due to your neglect to protecting the car.