Nice page. I came here looking for mention of meaning of 'debility house' on another page that linked to this, not having answers of its own.
No discussions so far on that here either, so with a bit of speculation mixed with common (rare?) sense I'll have at it:
Four possibles:
Prison (because he poached it).
Hospital (because he overdid the eating of it).
Workhouse (to repay other than by imprisonment for illgetting of it).
Asylum (now that I will leave to the speculations of others as I can't think of anything specific).

My own view is that is IS a silly song, bounded by fact, and is meant to be silly. In hard times, people do not waste. Suppose a man makes virtue of this, and brags. He eats it ALL (so he says), never mind that it makes him ill, earning promotion to 'debility hall' given the final doings... In reality, doctors being more expensive than food, no doubt some self-restraint was exercised, but it makes a better song this way, two nippers and all.