The body of the mother who killed her three children was discovered in the early hours of Monday at Rampton Hospital near Retford, Nottinghamshire.
It was reported yesterday that a priest, speaking on behalf of Riggi's family in California, said: "They feel a sense of relief. They now believe their sister is not being tormented."
It was also claimed that as well as a history of narcissistic, paranoid, and histrionic personality disorders, she had developed eating problems before her transfer from a psychiatric unit in Scotland after she had been moved from Cornton Vale near Stirling.
Reports also suggested she had died of natural causes.
American-born Riggi, 50, stabbed her children - eight-year-old twins Austin and Gianluca, and Cecilia, five -eight times at their second-floor flat in Edinburgh on August 4, 2010.
She then set off a gas explosion in a bid to cover up the killings, before leaping from the balcony in an apparent suicide attempt.
She survived her injuries and was charged with their murders. She later pled guilty on a reduced charge of culpable homicide on the grounds of diminished responsibility. She was jailed for 16 years in 2011.
A Nottinghamshire Police spokesman earlier said the death was "unexplained but non-suspicious".
The area's coroner suggested post-mortem examination results may not be available for a number of days.