Is that Tilda Swinton in the middle?
However, Microsoft has clarified the situation, noting, "People with dormant Windows Live IDs can continue to enjoy the benefits of their Xbox LIVE Gamertags on their Xbox 360 consoles, including earning Achievements; however, they will not be able to use their expired Windows Live IDs for activities such as account management on xbox.com." According to a company representative, "An Xbox LIVE Gamertag is unrecoverable from the system only when the associated Windows Live ID has become dormant and the Gamertag has been deleted from all Xbox 360 consoles." In other words, a dead Windows Live ID will prevent you from recovering your Gamertag online should you change consoles or attempt account management, such as renewing your Xbox Live subscription.
Microsoft is "actively working" on a solution that should allow you to sever the dead weight of an expired Windows Live ID and link your Gamertag to a new one. In the meantime, Major Nelson recommends you log into your Windows Live ID (do it through xbox.com) at least once every four months. Think of it as an insincere pleasantry with long-term benefits -- like visiting your mother-in-law.