If a kid gives you a verbal but refuses to sign in December, then you treat him like any other non-committed player. I would assume that ND has two types of offers. The must have - who is told that ND will hold a place open for him right till the end, and the wanted - a kid who is often told that they have multiple offers out for his spot, and the scholarship is given to the first one who commits.
For the must have recruit, nothing changes. ND will still recruit and hold a spot open. For the simply want recruit who gave a verbal but refused to sign in December, I think the coaches may have to reevaluate him. If he still wants to verbal, they may tell him that he is now 3rd on their list for his spot. They will only accept his verbal if Billy Jones or Joe Smith verbal elsewhere. Or they may simply accept his verbal once more and wait for the February signing date.
An early verbal who refuses to sign in December really puts the coaches in a tough spot. I personally would be wary of this recruit and would strongly question his desire to attend ND. Unless their is a wide talent gap between him and others on their recruiting board, I would simply move on. I would put him on the back burner and would only go back to him if others on my list committed elsewhere.