Kernel shouldn't crash, and anything running in memory will be okayish, but it definitely will get less and less stable. It won't be possible to start new processes.

I have a Linux install on a USB SSD with a flakey connection, if I bumped the cord the root would unmount. It was fairly resilient, but graphics would slowly start disappearing. I'm fairly sure I could cleanly reboot as long as I had a terminal open, but its been a while, so maybe I'm misremembering.

Still, the overall system becomes pretty useless, so i guess its fair to call it a crash