All of the keyboard-driven terminal signals can be intercepted; catching INT (^C) for cleanup is just more common than the others. Only KILL and STOP cannot be caught.

^Z sends TSTP (not STOP, though they have the same default behavior) to suspend; some programs catch this to do terminal state cleanup before re-raising it to accept the suspension. Catching it to do full backout doesn't make as much sense because the program anticipates being resumed.

^\ sends QUIT, which normally causes a core dump and is rarely caught. If you have core dumps disabled (via ulimit -c 0 or other system configuration) then you can often use it as a harder version of ^C; this is how I would tend to get out of ‘sl’ in places where I found it unwantedly installed.

For the most simple case of a single job, I use the job number (`[1]` in the example) with %-notation for the background jobs in kill (which is typically a shell builtin):

    $ cat
    ^Z[1] + Stopped                    cat
    $ kill %1

ctrl-z pauses the process, it doesn't terminate. I think of z as in zombie as you can then run fg to bring it back from paused state or as you suggested kill in it for good