If you have not paid your dues and fees for the timeshare, you are in default and it can be taken back by the timeshare company. A timeshare is like a mortgage; if you don't pay, they can take it back.
If you have a mortgage or other loan for the timeshare, or if it is listed as security for such a loan, then it can be foreclosed upon. A timeshare is real estate, and the rules are basically the same as those for a home.
The short answer to the question of can they foreclose on my timeshare is yes they can. You are buying not renting from the resort and they are not going to let you go without paying.
