Can it be possible to get tooth cavities from fake sugar?

No: If you mean artificial sweeteners like aspartame (nutrisweet) or splenda, then no. Bacteria need real sugar which they eat and produce acids which cause cavities.

Yes: Some "fake sugars" can be broken down by the bacteria that cause cavities.

No and yes: The artificial sweeteners cannot be metabolized by the bacteria which produce cavity causing acids. However, it is unlikely that you are only consuming those products. Sugars are found elsewhere in your diet - breads, pastas, crackers, fruits, etc. Be aware of your real sugar sources, decrease frequency of snacking, step up the brushing and flossing, and get regular dental checkups.