Not buried with their tombstone. I have never heard of that. Can you please elaborate or explain?
Easiest example is a stone for a husband and wife put up after the first one dies. The surviving spouse could end up being buried somewhere else--either because they moved or married again.
I assumed that my great-grandmother had died at home. The Health Department required the county of death to issue a death certificate and they could not find a certificate for her. Years later, I found out that she was sick and the family took her two counties over to the nearest hospital and she died there. I finally obtained the death certificate.
There are times, such as in a Military cemetery, where a memorial stone is placed for someone who is actually buried somewhere else or the body is missing altogether. This is also somewhat common in pioneer family plots if a family member has moved far away or is lost at sea.