Having administered dozens & dozens of LS Windows for DB plans, when this scenario occurred, we have consistently seen plan sponsors tell TV participants like this that they are out of luck, predominantly for the reasons CuseFan cited above (including eligibility being tied to a valid/current address on file).
Fortunately, this has been very, very rare given that we've handled LS Windows for over 100,000 participants, and our best practice is do conduct an address search for all members in the LS Window before materials are mailed, which minimizes this type of situation from happening.