The insurer files a cancellation notice, the SR-26, with the DMV, and the DMV is required to suspend the license again. Clearing it takes a new SR-22 and a $50 fee. Ask the DMV how the lapse affects your end date.
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. Under Neb. Rev. Stat. 60-544 the insurer cannot cancel a certified policy until at least ten days after mailing notice to you, and if the policy is not reinstated in that window the insurer files a notice with the DMV, which then suspends the license. The DMV says the suspension may be withdrawn if a new SR-22 takes effect on or before the suspension date, which is the whole case for acting inside those ten days. 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.