Change mail to make it store unsent emails?

That's the standard operation of an MTA. Mail is kept and retried at different intervals until it's able to deliver it. Look in your mail queue, for sendmail that's mailq(1).

Normally it's retried up to about 5 days before it gives up and bounces it back to the sender with an "undeliverable" message. In the mean time the sender will receive status messages that the mail cannot be delivered and will be retried at a later time.
 
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