I had a similar issue - the glass on the back of my Pixel (5 I think?) cracked right by the power button, and it seemed to be kind of OK but I got a new phone anyway, but left the old one in my glove box of my car where I used it for the bluetooth entry to the parking garage at work (and because re-enrolling was a pain). It didn't have the sim setup or wifi enabled so didn't think much of it.

This worked fine for a few months, just turning it on at the gate then off afterwards and threw it back in the glove compartment.

Until one day driving home I heard a weird beeping, then a voice from the glove box asking what my emergency was. I shouted back pulling over and fumbling to get the phone out, and told the responder my phone had called them by itself. I was a little surprised as I thought every call, even abandoned, had to be followed up on, in case there was coercion? But I guess not if you just blame the phone. I guess the buttons had shorted to turn the phone on, then ended up going into the emergency call? I couldn't even turn it off at that point as the power button refused to work and the digitizer was partially non-functional.

A bit of a pain, and a (hopefully small) waste of an emergency responder's time, but I can see this sort of thing being relatively common - in "normal use" I've had my phone somehow end up on the emergency call menu, just being jostled and unlocked or fat fingering the wrong buttons, so wouldn't be surprised if unneeded emergency calls are relatively common on even fully functional devices.

But I guess that cost is worth paying if it's more convenient and quick when there is an emergency?