Either parent can take over the family's subscription. If the one who's been paying wants to stop, the other can pick it up from Plan & billing before the term ends, and nothing lapses.
This also covers the harder case: one parent deleting their account, or simply disappearing. The family doesn't lose its plan because of whose card it was on.
Whoever takes over pays from that point. Nobody is billed for the part someone else already paid for.