The insurer notifies the state, and the state can suspend the driving privilege again. The proof period stops running until a new certificate is on file, so a lapse extends the obligation rather than pausing it harmlessly.
More detail
This is the mechanism that makes a filing different from ordinary insurance. A normal lapse is a coverage problem you fix by buying a new policy. A lapse under a filing is a licensing event, reported by the carrier, and it can undo months of progress. The most common cause is not a decision to cancel, it is a failed payment: an expired card, a changed bank account, a paycheck that landed late. Two defenses are worth setting up on day one. Put the policy on a payment method you monitor and set a calendar reminder a week before each due date. And if money is going to be short, call the producer before the payment fails rather than after, because moving to a cheaper policy form is a normal transaction while curing a reported lapse is not.