You can stop (pause) a running process by sending "-STOP" signal via kill command in Linux. You can re-run same stopped process again by sending "-CONT" signal to it. Assume that we have a process to stop and it's pid is 8674. Following, command will stop the running process id 8674.
# kill -STOP 8674
Now the process is stopped, to resume it's running state, you have to send "-CONT" signal.
# kill -CONT 8674
In Solaris, you can do the same task by using pstop and prun utilities or you can use kill command and use signals "SIGSTOP" and "SIGCONT".