I've certainly had something equivalent to the first one in Chrome frequently, seemingly when it's waiting for an unresponsive child process, often when closing a tab. It won't lock up as the UI seems to be separated from the other processes well enough to allow it to keep rendering loading animations etc. However every part of the browser will stop functioning including showing any tab content or opening any menu, for 10s of seconds at a time.

I've also had Chrome destroy my browser profile completely many times. It will start up and say something like 'your profile was unrecoverably corrupted and has been deleted'

Both are very complex pieces of software with lots of bugs.