Well, I found a new way to break a part, playing with Insert>Features>Shape.
Try this: Sketch a rectangle on the Front plane, extrude back to form a solid whose front face is coincident with the origin. Invoke the Shape command, select the front face to shape and then select the part origin as an item to constrain to. Adjust some of the option sliders to get an arbitrary shape. Finish the command.
Notice that the origin has left its usual place near the top of the feature tree and is now consumed in the shape feature as if it were an ordinary sketch. This should be a warning that all is not well. But wait, there's more.
Delete the shape feature and check the box to also delete absorbed features. After the feature is gone, so is the origin!
In this simple case, there are no warnings at all. But I first found this in a part with 20+ features, many of which were constrained in some way to the part origin. When I deleted the shape feature and the origin, the feature tree lit up with red cherries that got my attention so I was able to undo the delete and get the origin back. But if I had saved the part with errors, it would have been toast.
This one's already on the way to SW Corp. via Computer-Aided Products, in my opinion the best VAR in this arm of the galaxy.
Art Woodbury