additional terms
28.Members must remain eligible for this promotion at the time of travel. BA and Amex reserve the right to refuse to issue or honour any Companion Voucher in the event that the Member is in breach of the terms of the British Airways American Express Card or the BA Executive Club Membership.
I guess you become ineligible if you end the agreement for the card. Section 1 states must be a member of BAEC AND be the main account holder on the card.
1.You can only receive a Companion Voucher if you are a member of the British Airways Executive Club and are the main account holder within a British Airways American Express Credit Card account (a “Member”).
In practice it would be down to how good their systems are to spot/flag/police it.