Create a special emailing or mailing that is targeted specifically to this group that tries to get them to re-opt in to your subscriber list. There mailing list are a couple of different ways you can reengage old customers. You can send them a special offer that is only for previous customers.
You can send a message that states you are updating your database and ask them to take a moment to review and make sure their mailing list contact information is current. Surveys are another great way to garner attention and get a response from old customers. Anyone that doesn't respond should be deleted or separated from the rest of your mailing list.
Rather than focus your list building efforts elsewhere, take these three steps to build a quality list. It's always about quality over mailing list quantity because you will have a better conversion rate when you are communicating with subscribers that are actually interested in what you have to offer-each and every time.