A nonmember spouse temporary record is not movable. Temporary records only reside in the local MLS and not at the church administrative office. When a member married to a nonmember moves, the temporary record, if one was created, is not moved but removed from MLS (assumes no financial records are tied to that record number). But as you said there is no record, temporary or otherwise, for the nonmember spouse. You do not need to be concerned with moving a nonmember spouse if there is no record created.
Just for the information of some readers I will add this bit of information. There is a special record that is a membership record created at Church headquarters for nonmember family members (spouse, child, or parent). It is a
linked record. If the nonmember spouse has a record number that does not contain the unit number in it, then it most likely is a linked record. For the purposes of moving a nonmember spouse linked record with a member record, only the member spouse record needs to be moved. Church headquarters will automatically move the linked record when the member record is moved.
So your only concern now is to find what happened to the member's record.
If the record exists on your MLS you should be able to find it. I am going to assume that you can locate the member by going to Membership > Individual Record and type in their name. If so, then there is either a temporary record or a member record in your MLS. If not, then the record no longer resides in your MLS and the record has already been moved. If you did not move the record out then the gaining unit requested the record from their end.
If the household only consists of the member and nonmember spouse, you should try moving the household first. If you cannot locate the household by going to Membership > Move Household Records Out, then try Membership > Move Individual Record Out. You should be able to at least locate the member husband's record when moving an individual record.