If you look at census records from the 1920s and before, dorm residents in schools, seminaries, and institutions are referred to as "inmates." The term, then, was not limited just to prisons as today. How did the association of the word to prisons only, evolve? Has this evolved usage made the former, broader definition obsolete or inappropriate?
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):
From Noah Webster's Compendious Dictionary of the English Language (1806):
From Webster's American Dictionary of the English Language (1828):
From Merriam-Webster's American Dictionary of the English Language (1864):
From Joseph Worcester's Comprehensive Dictionary, Revised Edition (1873):
From Merriam-Webster's International Dictionary (1890):
From Merriam-Webster's First Collegiate Dictionary (1898):
From Merriam-Webster's Third Collegiate Dictionary (1916):
From Merriam-Webster's Fifth Collegiate Dictionary (1936):
From Merriam-Webster's Seventh Collegiate Dictionary (1963):
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."