With any foreclosure, the first thing is to sell the property. When I was on an HOA board, we bid in the amount owed, so there was no deficiency, and then got the week back, but that was a member controlled board. Developers may act differently. If they bid in a nominal amount, say one dollar, then that would leave a deficiancy for the rest of it, and they could get a deficiency judgment on that amount. I never heard of any OBX timeshare resort either member-controlled or developer controlled doing that, but one of our board members had become aware of a timeshare elsewhere doing it that way. I talked with board members at other resorts enough that I would have heard about it if anyone on the OBX was doing it.
One practical matter is that while the resort could sue in their local court and obtain a judgment, most timeshare owners would probably not have any property there, other than the timeshare, to collect out of. So what the resort would have to do is file a second lawsuit in the local court of the debtor to get "a judgment on a judgment", which is usually pretty simple, but involves local attorney fees, court costs, etc. in each debtor's local jurisdiction. That judgment could then be levied against their property. This additional complexity and the costs and time involved are a big reason resorts tend not to do this, but that does not mean they can't or won't.
My friend who practices consumer law says that many collection agencies are so sloppy that often one can avoid even getting to the lawsuit stage by challenging a debt claim at the letter stage and demanding copies of their proof of debt. If you get to the lawsuit stage, you can use discovery for the same purpose, but it is easier and cheaper if you can see them off at the letter stage. I suspect a Mexican organization would be a particular mess in their documentation.