Imagine a hacker gets a group of logins and passwords. (e.g. March 2013 EverNote incident). A email@example.com changes immediately his old password1 to password2 and checks an option - I will be carefull and use only the new password and also checks - notify me if password1 login attempt accurs. That way gmail does not set notice of what password1 was but only a statement that an attempt occurs. That way firstname.lastname@example.org knows that the attackers are really active and may be cracking his other accounts.
Also assume that gmail, evernote, mint, dropbox and police are united in HuntDownHackerAttacksAliance.org and report to each other loginIDs that were compromised (limited to the aliance), so such aliance can see patterns that certain group of IP adresses tried to login using old passwords1 to exactly compromised group of gmail users1tos users8000 (reported by EverNote to the alience for gmail subset of the EverNote attack).
Is it possible to Gmail to offer such notification service?