How did "inmate" evolve to only apply to prisons and asylums?

Perhaps the simplest way to observe the evolution of inmate is to note the definitions that dictionaries have assigned to the term through the years. Here are the relevant ones that I have at hand.

From Samuel Johnson's Dictionary of the English Language (1756):

Inmates are those that be admitted to dwell for their money jointly with another man.

From Noah Webster's Compendious Dictionary of the English Language (1806):

a lodger, one who lives in the same house.

From Webster's American Dictionary of the English Language (1828):

A person who lodges or dwells in the same house with another, occupying different rooms, but using the same door for passing in and out of the house.

2. A lodger; one who lives with a family, but is not otherwise connected with it than as a lodger.

From Merriam-Webster's American Dictionary of the English Language (1864):

A person who lodges or dwells in the same apartment or house with another; a fellow-lodger.

From Joseph Worcester's Comprehensive Dictionary, Revised Edition (1873):

One who dwells jointly with another; a fellow-lodger; a fellow-boarder.

From Merriam-Webster's International Dictionary (1890):

One who lives in the same house or apartment with another; a fellow lodger; esp., one of the occupants of an asylum, hospital, or prison; by extension, one who occupies or lodges in any place or dwelling.

From Merriam-Webster's First Collegiate Dictionary (1898):

A fellow lodger; esp. an occupant of an asylum, prison, etc.; also, one who occupies or lodges in any place.

From Merriam-Webster's Third Collegiate Dictionary (1916):

1. One who lives in the same house or apartment with another. 2. One of a family or community occupying a single dwelling; also, one kept in an asylum, prison, etc. 3. An inhabitant.

From Merriam-Webster's Fifth Collegiate Dictionary (1936):

1. One who lives in the same house or apartment with another. 2. One of a family or community occupying a single dwelling or home; now esp., one kept in an institution. 3. An inhabitant.

From Merriam-Webster's Seventh Collegiate Dictionary (1963):

one of a family or other group occupying a single residence; esp: a person confined in an asylum, prison, or poorhouse

The definition of inmate has changed very little in the four subsequent editions of Merriam-Webster's Collegiate Dictionary series.

Evidently the biggest shift in popular understanding of the term (in the United States) occurred between 1864 and 1890, when the sense of "lodger" was supplemented with a new meaning: "one of the occupants of an asylum, hospital, or prison."

I note, too, that the terms roommate (dated to 1770) and housemate (dated to circa 1810) made their Merriam-Webster's debuts in the 1890 International Dictionary and the 1973 Eighth Collegiate, respectively.

As a way of referring to a lodger or paying housemate, I think, the term inmate is virtually obsolete today. That sense of the word has simply been overwhelmed by the meaning "incarcerated or otherwise institutionalized occupant."