This problem can be reproduced with a simple pipeline job that does nothing but echo and sleep in a loop.
1) Start a run of the pipeline job, the job produces output in the Console Output as I expect
2) Put Jenkins in "Preparing for Shutdown" mode. The jobs stop producing output. That's somewhat surprising, as runs that were started before entering Shutdown Mode are usually allowed to complete.
3) Cancel "Shutdown Mode." The job is still "stuck" and doesn't produce any output. The job also cannot be canceled except by a "hard kill," i.e. going through the "Forcibly terminate running steps" and "Forcibly kill entire build" links
The behavior in #2 is surprising, but not really a problem for me. However, the fact that entering and leaving shutdown mode completely hoses running jobs is really bad. This is compounded by an init.groovy script we use that places Jenkins in shutdown mode at startup.