Dean Saunders died at HMP Chelmsford in Essex in January 2016.
The 25-year-old had been arrested the month before, after his father was stabbed during a paranoid episode.
Care UK, the healthcare provider at HMP Chelmsford, announced it is to quit its contract at the prison.
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It made the announcement after the jury's critical narrative conclusion.
The company said it had attempted to resolve issues at Chelmsford Prison but the level of resources the prison planned to make available were "insufficient".
Mr Saunders, from Basildon, was a stay-at-home father, described by his friends as a "generous man" who loved his family.
He had been briefly held in a mental health secure unit in Rochford.
After he was released from hospital, he became "paranoid and confused" and attacked his brother and father in December 2015.
He was then charged with attempted murder.
The jury concluded he killed himself "while the balance of his mind was disturbed, contributed to by neglect".
The two-week inquest heard that he was unable to speak to his family while he was in prison because telephone numbers were taken down incorrectly.
The jury unanimously concluded that "financial considerations" were made in deciding to downgrade Mr Saunders from constant watch to half-hourly observations.
It said there were "multiple failings" including an "wholly inconsistent" review system and a "complacent" approach to Mr Saunders' state of mind.
The jury also found an assessment of his mental health needs was "not adequately conducted" and there were "multiple failings in recording and passing on information".
Mr Saunders was one of 102 inmates known to have taken their own lives at prisons in England and Wales in 2015.
An inmate who killed himself and his family were "let down by a number of failings" by the prison system and mental health services, an inquest jury has concluded.