Many people refer to it as "relay theft" since historically it's often just a matter of relaying/repeating a signal - there may be no real authentication involved.
Around physical security, I'm often reminded that "locks are for honest thieves".
Anyone can break a window to steal your stuff, getting a duplicate immobilizer chip is hard and usually requires an inside man in a dealer network.
Unless you talk to the car's ECUs over the diagnostic port and read out the secret values for creating a duplicate or outright patch out the immobilizer check in the firmware. There's usually no auth on this and it's just obscurity, which I expect to already be broken and exploited by tools available on the black market.
I can't imagine any car would stop if it lost signal with immobilizer chip- that would be a safety problem. That is how relay attacks work- signal is required only for a brief period.
So it's wireless... So someone can still use a relay attack to send the signal from the start button to the keys hanging up by your front door...
The only exception is if I have full control over it, including the ability to lock it down. No OTA updates; if I want to install security patches, it'll be through Ethernet or USB or some other wired connection. But preferably, there wouldn't be a whole lot of software to update in the first place.
That seems to me to be far more secure than a modern tesla.
There's far less chance of leaving your key in the car if you have to press the lock button on the fob after you get out -- done that on hire cars before. The key is always in the same place.
Conversely you can leave the key in the ignition if you're popping into the store to pay for the gas and leaving your passengers in the car. I had a keyless fob on another hire car in my pocket, alarm went off when I went into the store.
I don't get the appeal of keyless.
And modern cars absolutely know how to switch safely to a "limp mode" that lets you pull over safely.
Many manufacturers have actually worked to improve wireless key security. Including Tesla. But this is a new class of attack on the key fob.