Depends on what functionality you have... I'd say this isn't a really good situation.

Check the  aspnet_Membership table of your database to see if the email addresses you need aren't hanging around in there. If they are you could write a SQL script to sync them up.

Otherwise my advice...

1) Upgrade to 4.9.3 if you haven't already... backup and make sure your modules work.
2) Fix your provider problem so it doesn't happen in future.
3) Compile a list of subscribers without email addresses.
4) Disable their accounts.

You then decide what to do:

1) Contact the subscriber and ask them to send you an email... think of an excuse
2) Wait for them to contact you when they can't log in. Tell them for security reasons you need their name and email address in order to fix their problem.
3) Review backups or other sources you might have and enter in the data yourself.

You can then update and re-enable their accounts one by one.

Good luck...

That's quite clever.. I would never have thought of that one!!!