What was meant by 'Debility House', as in a Yetties song?

Debility: The state of being weak or feeble; infirmity.

A planet in detriment or fall is in a precarious condition, more so if it is peregrine or otherwise afflicted. In horary the use of this symbolism is often remarkably literal and can be used to describe someone who has 'fallen' from grace or is incapable of maneuvering a situation to their advantage. In charts drawn to find a missing object, for example, a significator in detriment may suggest the object has been damaged; in its sign of fall it may have physically fallen to the floor. To have many planets debilitated in this way in a nativity is considered a sign of obscurity and low birth.

More:

http://www.skyscript.co.uk/dignities.html

https://dictionary.cambridge.org/dictionary/english/debility

The Yetties are a folk group from Dorset, England. They sing an old song about eating bits of a mallard. "Oh I have et the leg of a mallard, etc" All the verses end with the line "And now I am in debility house, and good-o meat was the mallard".
I suspect that the reference is to the workhouse, but I haven't been able to find any definite reference to it.
I'm pretty sure there is no astrological connection.

Here's a little more on your version:

http://www.mudcat.org/thread.cfm?threadid=84022