Could a bone scan pick up on dead cancer cells after one has been treated for bone cancer?

No: Bone scan is a crude way of measuring active disease in bone. There are more sensitive tests available now. It does not pick up dead cells. But not showing active disease in an area where it was showing disease, "lack of uptake" is a good sign.

Sometimes: Complete lack of uptake by a bone scan can indicate lack of metabolism after cancer cells have been killed. We often see this after people have received radiation therapy (low tracer uptake by the spine very common). Normalization of the bone scan is reassuring. You might want to look into a 18f-fluoride pet/ct bone scan.