I just did exactly the scenario the OP asks about, and the result was that all subsequent jobs hang on a sh step for 5 minutes and then get this error:
17:36:31 process apparently never started in /var/lib/jenkins/workspace/TesiraFirmwareNG_develop-tmp/durable-6a718028
17:36:31 (running Jenkins temporarily with -Dorg.jenkinsci.plugins.durabletask.BourneShellScript.LAUNCH_DIAGNOSTICS=true might make the problem clearer)
Anyone know what this is? The purpose of the Durable Task plugin appears to be to enable Jenkins to monitor long running tasks outside Jenkins. Reading this, I believed it to be a key part of how Jenkins manages slaves and their jobs. And that perhaps rebooting the Jenkins slave that had been running the downstream job when I rebooted the Jenkins master, would resolve the durable task problem.
But no luck - after rebooting master and slave I'm still getting the same "process apparently never started" error above. Anyone know the cause of this issue, or know a solution?
UPDATE: Our problem turned out to be an empty environment variable in Jenkins global properties, and nothing to do with slave jobs running when its master restarts. This issue was our cause, and it was only evident after enabling LAUNCH_DIAGNOSTICS java arg, which resulted in more output that showed previously silent errors (empty environment variable passed to docker call) which lead us to root cause.