Short answer. The case does not stall. If, despite all efforts, his attendance cannot be secured, the court may proceed ex parte and decide as the facts warrant. But the judge is directed to endeavour to protect the interests of the non-appearing spouse.
What the law says
If, despite all efforts, the attendance of the non-consenting spouse is not secured, the court may proceed ex parte and render judgment as the facts and circumstances may warrant. In any case, the judge shall endeavor to protect the interests of the non-appearing spouse.
Family Code, Article 245 — Proceeding Ex Parte to Protect the Absent Spouse. Read the full provision →
Non-appearance is not a veto
The fear behind this question is that a spouse can block a needed transaction forever simply by ignoring the mail, and the article answers it. The court may proceed ex parte — that is, on the petitioner's side of the case alone — and render judgment. The result is a real judgment, not a provisional one. So the strategy of staying away does not preserve the status quo; it forfeits the chance to be heard while the case proceeds to a decision anyway.
'Despite all efforts' is a condition you must satisfy
The permission is not immediate. It arises only where attendance is not secured despite all efforts, which puts a burden on the petitioner and on the court before the case can go forward one-sided. This is the same concern that makes proof of notice a condition of the court's exercise of jurisdiction over the petition. Expect to account for what was actually done to reach him: where notice was sent, what was returned, who was asked, and what you know of his whereabouts. Thin efforts invite an order to try again rather than leave to proceed.
The judge is not on your side either
The second sentence is the part petitioners underestimate. The judge shall endeavor to protect the interests of the non-appearing spouse, which converts an uncontested hearing into something other than a formality. Nobody is there to test your case, so the court itself will — probing the price, the terms, the necessity of the transaction, and whether the absent spouse's share is preserved. Judgment is rendered as the facts and circumstances may warrant, so a proposal that looks unfair to the absent spouse can be refused or approved on modified terms.
Build the record as though he were watching
The practical lesson follows from that duty: prepare the ex parte hearing as if the other side were present. Have an independent basis for the value of the property and the fairness of the terms, be able to explain what happens to the proceeds and how his interest is preserved, and document the search for him thoroughly as you go. A petition that answers those questions before they are asked is the one that moves; a bare assertion that a sale is necessary tends not to.