In the converse I have never heard of a case being won (ultimately) by passengers breaching their contact with airline's having sequential / complete use of coupons provisions. In a few case low courts have agreed with the passenger, but these have always (?) been overturned.
There is a history of airlines winning the cases, but usually when it was the first flight rather than the last (and with the passenger suing the airline after being denied boarding). I would imagine that when airlines do find repeated abuse (my term) they would not resort to the courts, but would find other ways of having the passenger cease and desist. A polite letter to begin with ...
I could almost envision the passenger being met on arrival at Heathrow by a very large 'customer service representative' who would escort the passenger to their connecting flight ...
The question is what the contract provides, including what the contract provides that you will pay the airline if you do not do what you have promised to do.
BA's Conditions of Carriage say that they will not carry you on subsequent flights, until you have paid any difference. They don't limit this to subsequent flights on the ticket in question, but to any future flights.