I agree with Dave_C: it appears one account can expire independently of the others although BA use cease (passive) instead of terminate:
16.1.13 If a participant dies, ceases to reside at the Household Account address or ceases to be a Member of the British Airways Executive Club, the unredeemed Mileage held by that person will be removed from the Household Account balance.
And no activity may well close the account, not just cause the milage to expire:
3.12 Membership will terminate automatically:
3.12.1 in the event of the expiry of all Mileage in accordance with Clause 12.3 when a Member has not earned or redeemed Mileage for 36 consecutive months