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Then consider getting a box to keep the fob in inside the house. Thieves are getting re-transmitters for less than 20 bucks, can walk up to your car and make the fob inside your house unlock your doors or drive away in your car.  
 
The reason this works is the fob and the car have to talk to eachother. The fob has a long range (so you can unlock the doors from further away, set of the panic alarm, etc) but the transmitter in the car is short range, so it can only reach the fob when it is right beside it. The fob then sends a signal back to the completing the "circuit". The re-transmitter boosts the signal from the car to reach the fob in your house to make the car think its right beside it and unlocks the doors.  
 
So, find a cheap faraday bag to put your "keys" in when not in use.

Source?

My GM product has a factory installed autostart and door lock system with the key fob. It may start the car and unlock the doors, but the key must be in the ignition and the car restarted before it can be moved.

The op means a keyless car that just had a fob. Like my wife's edge there is no ignition to put keys into the fob simply must be near by and the door will unlock when you grab the handle and the key must be inside the doors to start the car by pushing the button

ultraguy said "Source? "

http://www.nytimes.com/2015/04/16/style/keeping-your-car-safe-from-electronic-thieves.html?_r=0  
 
http://www.networkworld.com/article/2909589/microsoft-subnet/thieves-can-use-17-power-amplifier-to-break-into-cars-with-remote-keyless-systems.html  
 

The hacks requires a relay to push the weak signal from the car back to the key fob in your house. The result is the two items can talk to each other. If they get too far apart, the car stops.  
 
Yes, they can start your and drive it, but the problem for the hack is range.  
 
The car can only go as far as the manufactures original key fob reaches when you try to unlock the car.