When somebody cancels a subscription in the proper way, their card changes to a FTV card. This is presumably in the hope that one day they will resubscribe.
Sky will kill a card (rather than convert it) if:
(1) There is a breach of the T&C (i.e. they get to know the card is being used outside of the UK). I have, not surprisingly, seen a lot of this.
(2) The card is reported damaged, lost or not working and a duplicate requested. The card is killed immediately - before the subscriber gets their new one - to avoid any possibility of both cards being used at the same time.
(3) Sometimes when the subscriber simply stops paying (as opposed to cancelling properly). I don't know Sky's rules on this; all I know is that sometimes it happens and sometimes the card just goes FTV.
In the world at large (as opposed to my little corner), (2) is the most common reason.
Using the card in a Dreambox won't affect it - Sky have no way of knowing where, or if a card is being used except when it's in a digibox which makes a callback. Even then, unless you have multiroom where you must display the number to Sky and it's noted, a callback only confirms it is in use, not where.