The part is unselectable? Might be helpful if you upload the part file.
I started with one Protrusion, brought in another body as an Interpart Copy, used the break command to break from the original. This created a Face Set and a Construction Body of this Interpart Copy. I then toggled the Construction Body to a Design Body and this new Design Body can't be activated - it's grayed out. This created two Solid Bodies (the face set still exists in feature list) . I then joined both Solid Bodies with the Union command. So the Design Bodies go away and the part becomes just the Face Set which still exists last in the feature list and is unselectable in Assembly.
I've since Split the part into two Solid Bodies at a different spot, and now I have two Design Bodies and everything is selectable now so it's fixed. But I'm curious as to why the Union of a face set and a Protrusion produced a Face Set that was unselectable.
That part has one design body and one construction body. Neither of which are able to be toggled to the other mode. In other words, it's messed up.
I insert part copied it to a new part and got a usable part with two design bodies.