Is it possible to fall to a deep coma from a medically induced coma?

Medical coma: Medically induced coma is typically done in a setting to, protect body parts during injury, such as to brain after trauma, to limit damage. This is really like surgical anesthesia, and done in a controlled setting.With close monitoring. Your statement of a deep coma, really doesn't follow. If the patient had coma persisting after the induced coma were stopped, it would be from the initial injury.

No you can't: By deep coma, i assume you mean a prolonged coma that is not reversible. If that is correct, then a medically induced coma cannot cause a deep coma because the medically induced coma would stop when the nurses stop the medications used to induce the coma.