The User Custom Field should handle users being deleted.

If you try to delete a JIRA user who is the assignee or reporter of an issue, then you will not be allowed.
However, you can currently delete users that are referred to in Custom Fields.
When this happens, JIRA remembers the username that the field was set to, but when you view the issue, it is not displayed, and a Warning message will appear in the logs like:

WARN [issue.customfields.impl.AbstractSingleFieldType] Issue RAT-10 has an invalid value 'fred' stored in the field 'Dude'. User 'fred' was not found in the system.

This should be handled better, by one of the following:
1. JIRA allows custom fields to veto the user delete, just like reporter and assignee fields
2. If the user is deleted, the User Custom field can still display the old username, and not log warnings.
3. if the user is deleted, the user Custom field acts as though the username was deleted from its value, and it doesn't log warnings.
Note that 3. is probably the easiest to achieve, and closest to the current behaviour.