During a police pursuit, a suspect points a gun at his own head, effectively taking himself hostage.

Thus the police are in a predicament, as they cannot shoot the suspect who is now a hostage himself, and they risk him pulling the trigger if they pursue him.
Sherriff: Damnit Doofy, why'd you let the suspect run into the woods, we lost him!

Officer Doofy: He pulled a polish hostage, there was nothing I could do.
by Dr. Roboto August 17, 2021
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Another term for a person wanting to attempt suicide, usually involving police intervention.
Officer Smith had to respond to the high railroad bridge over the river- There was a polish hostage up there threatening to jump.
by Someone unlisted November 17, 2010
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