I don't know of a built in way to do this, especially because sometimes a user's password isn't even stored in JIRA. (It may be fetched from LDAP, Active Directory, or a third party authentication service like Google Apps or Atlassian's Crowd.)
But, there's an "updated_date" field in the cwd_user database table that you might be able to leverage.
Maybe someone else in the Community has other ideas to share?
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