I was about ready to murder somebody the second time I ran into that, but some googling gave me the reason: it happens (on GNU/Linux) when you have updated firefox, but you are running the old program. Since opening a new tab opens a new process, this effectively means the old system would have to work intimately with a newer version -- which is too hard.
The solution is the same as always: don't upgrade until you are ready to reboot the system anyways. Or don't upgrade at all, if you can get away with it.
Sometimes I open Chrome, not after any kind of abnormal force-close, and it says something like “your browser profile was corrupt and has been permanently deleted”.
Have you ever applied any of the about:config settings from one of those harmful “privacy” guides? Are you using an enterprise or school managed computer?
That's interesting, I've never had issues getting old sessions back. You could try recovering it via "History > Recently closed windows", it should be there usually.
I've never had this happen personally. What OS is this? I use Firefox on OSX installed through Homebrew, so I have to manually update it with brew. Firefox has never asked me to update.
For this reason I don't trust it when I'm doing meaningful work.