Ellen, Yes if you buy into one that works that way. Hugh has an explanation of both types on his website and an example of how to figure out whether it's financially beneficial to buy. It's www.arubahouse.com
You'll have to scroll down past all his house photos and other stuff to find it.

Only two timeshares in Aruba actually have deeded property. Its been explained to me that the Government doesn't deed property within one mile of the ocean. They only lease the land for a period of 60 years, however some resorts have a 30 year leases on the land. At the end of this period of time the government has 2 choices; 1) re-lease the land to the resort or 2) take the land back and pay the organization for all the improvements to the land.
All timeshares on the island that I am familar with (LaCabana, Costalinda, Paradise Beach Villas & Marriott) is life time ownership, with the caviot of the 60 year lease on the land.

I hope this info helps.