Here’s how I understand the issue:
A keyfob is a radio Transmitter. To unlock your car you need the radio transmission to reach the car. The keyfob doesn’t transmit a signal when at rest. Therefore putting a keyfob in a Faraday bag achieves nothing.
I don’t know where you got the idea that the key fob doesn’t transmit a signal when at rest. If you’re talking about keyless ignition with the button on the car (not remote start via key fob) the key fob transmits a response when it gets a request from the car.
The bad guys have a clever trick, though. They put one guy in your car and one guy next to you. The guy at the car hits the ignition button transmits the signal to the other guy, who transmits it to your fob. The second guy then transmits the response from your fob back to the guy in the car, who then sends it to the car. As far as your car knows, the fob is in the car. So it starts. A Faraday cage can protect against this.