Usually if the meeting of creditors is missed, the trustee will set another date for both spouses to show again. If the second one is missed, then that party is usually dismissed from the case after a motion and hearing.
The spouse who did attend probably could continue with the case.
I have also seen situations where the trustee questions the one spouse and continues the hearing for the other spouse (this is more common in cases where credits actually appear). You might be able to make arrangements with a trustee if there is an extraordinary circumstance. For example, I had a client who had just received a kidney transplant and was not allowed out of the hospital. The trustee allowed her son to appear at the continued meeting with an appropriate power of attorney.
I hope that helps!
Disclaimer: Attorney's response is not intended as legal advice and is for information purposes only. Inquirer should seek the counsel of a duly licensed attorney within that jurisdiction.
The answer depends on the jurisdiction and the reason. If the spouse just did not appear, the trustee may certify the case for dismissal with respect to that spouse. A bankruptcy judge would then hold a hearing and determine whether to dismiss with respect to that spouse. The other spouse's case could continue.