You sort of have the right idea, but that is not technically how it works. In the divorce, you can seek a court order to sell the house or perhaps buy out your husband's interest. If he won't cooperate and sign documents, the Court Clerk can sign them. If your husband fails to make payments, you can seek reimbursement for his failure to pay his share, however, he can seek an offset for your exclusive use of the residence.

First off it will depend on whether it is a voluntary default, negligent default, or involuntary. Often if the couple can work out a settlment, the petitioner submits a signed marital settlement agreement and the respondent just defaults. If the default is taken because the default is involuntary because the respondent didn't get actual notice, didn't understand rights and obligations or otherwise would have responded if they had known how and what to do, the default is almost inevitably set aside. In between is where the respondent basically just blows it off. I think that is the kind of default you are asking about. In that case you don't get any special treatment in your favor. Community property is still divided 50/50. You each still get to keep any separate property, etc. The advantage you DO get is you get to tell your view of things and the respondent does not. So, for example, if you ask for the house to be ordered sold, he would not get a chance to ask to buy you out instead. Or if you each wanted to buy the other out, you would win that dispute, and your valuation numbers (as long as they were reasonable and in good faith) would be used to calculate the buy-out. Bear in mind, though, that courts really hate to have cases decided by default and will bend over backward AND into a pretzel to let a defaulting party get relieved of the default and present their case. Only if the default is really knowing and willful, almost amounting to contempt, will it stand in the face of a respondent's request that it be set aside so the respondent can appear and present his case.