Why does my remote process still run after killing an ssh session?

"This behaviour stems from the lack of a controlling terminal for the running process. When the remote process does not have a controlling terminal, the remote ssh process handling your session is unable to kill the command, which is left hanging in a zombie state to be eventually cleaned up by init.

You can get around this by running it with a -t option, which gives it a controlling terminal. This will cause the process to terminate when you ctrl-c your ssh command remotely.

The -t option:

Force pseudo-tty allocation. This can be used to execute arbitrary
screen-based
programs on a remote
machine, which can be very useful, e.g. when implementing
menu services. Multiple -t options
force tty
allocation, even if ssh has no local tty.

Have a look at man ssh and man sshd when you use this option as there are other implications of having a controlling terminal, e.g. the ability to send escape characters."