Linux – Is a process PID guaranteed to stay the same as long as the process doesn’t die

Your process is probably dead but it still show up in the process table entry because it is a "zombie process". When a child process terminated and completely disappeared (except its process table entry) and the parent wouldnt be able to fetch its termination status (thru any of the wait functions), it is called zombie... Killing (thru signal) a zombie wont work because it is already terminated. What you need to do is find out its parent process and kill thjat one cleany, thus not using kill - 9

here are two simple steps to kill a zombie...

1. if the parent is still alive, try to kill it (or SIGHUP is all you need)
2. if number 1 fails, there is a bug in the kernel.... reboot is your friend and fix that bug :->

After reading your last comment I understand you want to know the PID of the process you are looking in your terminal. We have all this same need.
This is what I usually do:

I open two terminals.

In the first one I will read the output of mysqld:

touch   mysql.log
tail -f mysql.log

In the second one I run mysqld in background:

mysqld >mysql.log 2>&1 &
ps f

I use this second terminal to control/spy mysqld.

Hope this may help.
Cheers.