In both scenarios:
SSH access
Direct access
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Sign up to join this communityBackground processes will be killed.
You have to use "nohup" or "screen" to keep them alive.
If you're using bash, you also have access to the 'disown' built-in which dissasociates all backgrounded jobs from the current session. That will let you quit your current session and have them continue on. You won't be able to foreground those jobs in another shell so if that's your aim you'll need to look at screen.
The disown command is useful however if you started the job in the background and don't want to have it exit when you log out or close your terminal.
I'm not sure what exactly you're trying to accomplish, but have you tried running the "Screen" command?
http://www.rackaid.com/resources/linux-tutorials/general-tutorials/using-screen/
You really should be using "screen" as already proposed.
But technically a process will continue running if you backgrounded it with "&" and it does not do any input or output to the no-longer-existing terminal.