Are you sure? What if you inventing a "phantom partner" for each person, who represents "not getting married". The preferences for that phantom partner would b

Are you sure? What if you inventing a "phantom partner" for each person, who represents "not getting married". The preferences for that phantom partner would be 1. The person they are phantoming 2-N+1. All other phantom partners N+1-2N+1. All other people. If the person prefers not being married over all other available partners, then that will necessarily be a stable marriage. If they don't then the phantom partner will be able to find a match among the other unmatched phantom partners.