The train bodies do indeed consist of a stack of 4x4 "blocks" that were fully enclosed when assembled - and as I recall, we could fit a seated Duplo character within most of the cab sections.
Toby and the coaches had the most room, but most engines just about had room.
My back wheels do the same thing. There is no metal axle that connects both back wheels like the axle design does for the front wheels, but I'm sure LEGO designed it that way.
So, imagine the train's motor being in an "ON" state just a rolling. Now enters a kid, just being a kid. Grabs the thing, and starts a rolling in whichever direction kiddie wants ...
Don't have too much experience with DUPLO, so my suggestion is based on my limited knowledge.
I'm not aware if there a way to attach pig directly to LEGO bricks, however I thought of a workaround. Here, green DUPLO figure legs represent your pig feet.
FOLLOW UP POSTED AS AN ANSWER
So, I managed to disassemble the wheel axle from the gear axle, which show what I was expecting, a broken piece in the freewheel.
As my question is on how to disassemble the wheel itself @Rin Rio-Oki answer is the correct one.
A picture is worth a thousand words so put picture ...
The wheel axle is simply force in the gear ...