I see other CI systems with a Quarantine feature for their JUnit testing.
How about Jenkins keeps pace?
Quarantine is a reporting feature. The idea of the feature is that intermittent or misbehaving tests can be quarantined. This means that they wouldn't be reported in the totals of passing/failing tests and would not affect the pass/fail status of the Jenkins job. The tests can later be removed from quarantine when they are consistently passing or otherwise behaving well.
The quarantine feature wouldn't change whether a test executes, but rather how it is reported.