It would be nice, and should be possible for slaves to work disconnected through, say, a Jenkins restart.

The ideal scenario of course is a graceful shutdown where Jenkins can tell the slaves it's going to be shutting down but even an ungraceful stop of Jenkins, or the Jenkins machine or a network interruption between them should be survivable.

A slave could, in any of the above events (i.e. being told Jenkins is shutting down, or getting an error writing to the Jenkins server) just switch to writing the stdout/stderr of whatever it is running to a local file and then in the background periodically trying to re-connect to the Jenkins server.

The Jenkins server, through a graceful or ungraceful restart could establish and resurrect the jobs it was running when it was stopped and allow slaves to reconnect and dump their local buffering of it's child's stdout/stderr and then resume logging them to Jenkins.

I am sure the devil is in the details, but it should be doable.