To clarify further: If you play Falling Away and target either the 2- or 3-liner it deducts both points from the person that rescued it (or persons if it's the 2-liner and they each rescued half), but it retains one of the rescues as "stored" on the card (because Falling Away only removes 1 Redeemed Soul). If it was the 2-liner and 2 players each had half, the player who Falling Away was NOT played against is the one that retains their "rescued half."
To answer your second question, cards do not reset just by changing control. The 2- and 3-liners only erase half-rescues if they are discarded, returned to hand, or returned to deck.
