My thought was that the worst possible scenario was the fob being somewhere close enough to the car that they can chat, possibly with difficulty so they keep trying. Like somebody having the car securely in a garage, but the key is just through the wall. But I can't really see that being the case...
The fobs have to have some electronics active to "listen" for signals (in case it is the moment when you are by the car and you've pressed the door button). In theory I can't see why the car would transmit anything for the fob to hear and respond to unless a door button gets pressed. So the activation process should be:
Fob always receiving; car door button pressed; car transmits a request for the fob to respond; fob receives and identifies that it is the right car; fob responds with a code which means the car knows it is a paired fob; car unlocks.
This only needs the fob to receive nearly all of the time - but even "nearly all of the time" may mean it is 950 milliseconds of every second, so that the owner's impression is that it took less than a second to unlock. The car only needs to transmit in order to validate an unlock button press. The less it transmits the less chance of hackers tuning into the RF and attempting cracks of the exchange.
We keep our keys in Faraday pouches, a long way from the street-parked car, so car and fob would struggle to make any contact! Car and fobs are a few weeks short of two years and counting.