the machine that fits into a case is not exactly the same as the one that came with the Library Cabinet Combination. It's lighter and the base/bottom is different because the cabinet model has a built in controller that runs by the lever in the cabinet.
You can put a case made machine into a cabinet just like any other Singer, however if you have the cabinet model, then it's got a few quirks and you do need a specific type of lever to control it.
This is the underside of the Cabinet model - that part with the holes - is the "foot controller" there is a small round hole that a push pin on the knee lever pushes into to activate it.
My husband bought a second 101 for parts, and I was surprised to see how different they were. (we still have the parts he stripped off too).