L. Ron Hubbard, founder of Scientology, wrote several "bulletins" about his
process that he declared "Its results are nothing short of miraculous." The
three bulletins I'll be quoting from are:
1) HCO Bulletin 23 January 1974 "The Technical Breakthrough of 1973! The Introspection RD"
2) HCO Bulletin of 20 February 1974 "Introspection RD Additional Steps"
3) HCO Bulletin of 6 March 1974 "Introspection RD Second Addition; Information to C/Ses, Fixated Attention"
A "rundown" in Scientology is a series of prescribed steps designed to produce a certain end result. These steps involve "auditing", which is looking back through a person's past to find some memory that is causing the person present time problems. The Introspection Rundown is designed to handle a psychotic break or mental breakdown. The theory of the Introspection Rundown is that if you can find what caused the person to become introverted and psychotic then you can handle that cause and break the psychotic episode.
The first step of the rundown is "isolate the person wholly with all attendants completely muzzled (no speech)."  Auditing sessions are given infrequently to search for the cause of the psychotic break during this rundown, otherwise the person is isolated in complete silence.
"When it is obvious the person is out of his psychosis and up to the responsibility of living with others his isolation is ended."  The supervisor in charge of the person being isolated tests the person's condition by writing a note, such as "'Dear Joe. What can you guarantee me if you are let out of isolation?'"  If Joe does not answer in writing satisfactorily, the supervisor must write back "'Dear Joe. I'm sorry but no go on coming out of isolation yet.'"  Of course, "this will elicit a protest from the person"  but the rundown is not over until the supervisor concludes that Joe has recognized what caused his psychotic break. Once the rundown is over, if the person is a Sea Org member (the elite corps that signs a billion year contract with the church), he/she is put on the RPF - a sort of manual labor detail, and is "told to make good." 
Hubbard was quite excited about the Introspection Rundown and declared "THIS MEANS THE LAST REASON TO HAVE PSYCHIATRY AROUND IS GONE."  Also, "I have made a technical breakthrough which possibly ranks with the major discoveries of the Twentieth Century." 
The evidence in Lisa McPherson's case points to her being put on the Introspection Rundown after her accident on November 18. Her behavior on that date was one of a person having a psychotic break, which would then require the IR. Her appearance at her death was of a person who had been held in isolation for some time. The actions of church members after her death indicates to me that probably the IR was poorly handled and Lisa died as a result.
Hubbard wrote that "This Rundown is very simple but cannot be flubbed, as that will compound the errors and cause further introspection in the pc."  In other words, this process if done incorrectly could actually make someone having a psychotic break get worse. Handling the Rundown "is very precise and even touchy business. There must be no mistakes and you cannot be heavy-handed on them." 
What right does the church have to incarcerate mentally unstable people? What training do they have to prevent injury to the unstable person? What recourse or input does the person incarcerated have? What critieria are used to decide that the isolation is no longer needed? What training do the supervisors get to make such a decision over the length of someone's incarceration? How many people have gotten worse instead of better? What happens if a person never gets better, since Scientology considers psychiatry to be quack science? How long can isolation be maintiained? Months? Years?