Oh, I see. All the wireless car keys I've seen need a button to be pressed to unlock the driver's door.[1] I'll have to watch out for buttonless keys when buying a car next, it seems a pretty unsafe concept in itself, e.g. loitering hijacker getting in the car before you do/with you, etc.

[1] You usually need to press the button a second time to unlock the remaining doors. There's also often a separate button to independently unlock the boot. A typical procedure is therefore: open boot with the relevant button, put shopping inside, close boot, take trolley back to the stand, walk back to the car, unlock only the driver's side, get in, lock door with button from the inside, drive off.

In my car you need the RF signal from the keyfob to be nearby to open/start it. Once the engine is running, it will keep running until you turn it off, or it runs out of gas, even if the keyfob is not present.

If you turn the ignition off and it can't "see" the key, it will give you a warning message on the display cluster and you have something like 20 seconds to re-start the car before you're locked out.

Some cars, like my VW, require the key fob to be in the car or the immobilizer shuts the car off after a very short distance. I believe all VW cars have this now, even the ones without keyless entry/ignition. This of course just slightly complicates the hack.