It may well be that a reason for disappearing was the financial consequences of losing his job, but I don't think the Building Society would have an interest in the house that was burnt down. That was on an allotment belonging to a Freehold Land Society. In that case money was borrowed by trustees to buy the whole of the land required for the Society which was then portioned out to allotment holders. Howard would be paying off the cost of his plot in instalments.
However, he had other property (he probably still owned the house in Freedom Road where they were living in 1861) and any of these could have involved a mortgage.
I just discovered I had failed to send this reply I was writing earlier...
Yes, they disappear so completely I think it's possible they changed their name.
Micah Hinchliff was the father you mention who was shown the SUTCLIFFE grave by HOWARD. In the reports of his evidence that I have seen he says he was not certain whether Howard was referring to his own sister or to that of his wife. The fact that Eve was called HOWARD on marriage suggests she was his own sister (they were both born in Bakewell).
I had seen that 1851 household but wasn't 100% convinced because of the differences compared to 1861 (surname, ages, occupation, birthplaces) though each difference individually wouldn't be unusual or rule out the possibility that they are the same couple.