Use the disown shell builtin to exit the shell but continue running already back grounded jobs. The syntax changes from shell to shell.

zsh
<code>
disown [ job ... ]
</code>
bash
<code>
disown [-ar] [-h] [jobspec ...]
</code>

Example:
<code>
foo &
disown %1
exit
</code>

Relevant commands:
  * find the parent pid
<code>
ps xao pid,ppid,comm | grep foo
</code>
  * get information on a process
<code>
ps aux | grep NNNN
</code>

Ref:-
  * https://www.slashroot.in/disown-command-linux-explained-example-usage - goes into the details; good explanation with relevant screenshots; has some typos;
  * relevant section in zsh documentation: http://zsh.sourceforge.net/Doc/Release/Shell-Builtin-Commands.html -> search for disown
  * relevant section in bash documentation: http://manpages.ubuntu.com/manpages/bionic/man7/bash-builtins.7.html -> search for disown -> go to the second hit

Note:- To attach a disowned job, the instructions in https://unix.stackexchange.com/questions/31824/how-do-i-attach-a-terminal-to-a-detached-process might be helpful. But I have not tried them.

tags | continue running the jobs in the background, detach