Make sure the drawing and any dependant parts/assy's are in session. After deleting your Family Table, rename the part. Save the drawing and any dependant parts/assy's. If you want a copy of the instance to be the generic in the drawing:
1. Make a new junk directory. Change your working directory to the junk directory.
2. Open the old drawing.
4. Erase all instances of old drawing/generic/instances from memory.
5. Open the backed up drawing.
7. Edit the family table, highlight the instance, RMB, Copy Instance to Generic.
8. Choose Edit>Delete Entire Table
9. Rename the part, choose in session for safety.
9. Rename the drawing, choose in session for safety.
10. Save the drawing.
11. Delete the backed up old drawing/part/formats.
* Once again, if the instance is in assy's, the assy's should be in session.