I'm Doug, and I'm very sorry to hear of your situation. My goal is to provide you with excellent service today. I have been a licensed attorney for more than 3 decades. Please don't confuse excellent service with a satisfactory outcome based on your wants and desires. I can only explain the law to you---not guarantee that you will be happy with the outcome---any more than a cancer surgeon can guarantee a cure.
While you can certainly stop paying, the chances that the lender will foreclose is very small---because in this day an age timeshares are for the most part financial holes that you throw money at. No one wants them except for first time naive buyers.
If you are willing to file for bankruptcy, you can discharge the debt. Otherwise you are pretty much stuck with it. So, try and make use of it, or rent it out for as much as you can.
You may reply back to me using the Reply link and I will be happy to continue to assist you until I am able to address your concerns, to your satisfaction.
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I wish you and yours the best in 2016,