Gmail – Does Gmail still have the option to import email from other email accounts

It may be useful a apps-script that daily monitors the dates of the last messages received in a label associated with an imported account . For instance:

• create al label for each imported account.
• daily check this labels and get the date of last message received.
• Send yourself an email if the date is too far from now.

First you will need to create a filter and set all those specific email addresses in its conditions, and set it up to apply a new label (say, "Family"), to all messages, including existing ones.

Then you can follow this tutorial but instead of dragging all folders into your new account you would need to drag only the label "Family" which contains all your desired messages

EDIT: There's also "Gmail Backup" which claims might help with this, but I have not tried it.