When can a rental car company report the car stolen if you are latte?

It depends on the company, and it depends on how late you are, and how much effort the company has made to contact you to arrange the return. Reporting a car stolen is a hassle for the rental agency, and they would prefer to avoid having to do it.

The company can, however, penalize you in other ways besides reporting the car stolen. Not the least among these is additional charges for the extra time you kept the car, and possibly fines for doing so without prior authorization.

If you want to keep your rental beyond the time originally negotiated on your contract, CALL your agent or rental branch and talk to them about it. They want to work it out with you, not give you a hard time.