Before he skips out of town your husband can execute a power of attorney. Under a specific power of attorney, he can designate another person to sign in his stead with respect to just that one transaction. This is not uncommon in the context of real estate closings.
The only other alternative is to reschedule the real estate closing until he comes back to town.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.