The Nebraska obligation stays with your Nebraska record until it is satisfied, even after you move. You generally have to keep a filing in place with Nebraska while also meeting the new state licensing requirements.
More detail
States share driving record information, so leaving does not erase an open obligation, and a new state will typically see an unresolved Nebraska action when you apply for a license there. What that means practically is that you may be maintaining a Nebraska filing on a policy written in another state, which is a real thing carriers do and a specific question to ask before you move. The wrong assumption is that a new address resets the record. The right sequence is to confirm with the Nebraska DMV what remains open, tell the producer where the vehicle will be garaged, and make sure the certificate keeps flowing to Nebraska for the remainder of the period.