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Messages are frozen when the mail server has determined it cannot do anything to deliver the message. (they can also be manually frozen).
Exim has option to set how long frozen messages are kept on the system.
On a Debian/Ubuntu based install the /etc/exim4/conf.d/main/02_exim4-config_options file has the option timeout_frozen_after = 7d . Which means messages frozen for 7 days will get expunged.