Riggi, 49, originally from California, was found dead at Rampton Secure Hospital in Nottinghamshire, this week. She had been transferred there from Scotland, where she was serving 16 years for killing her children in Edinburgh in 2010.
It had been hoped she would give evidence by video link at a case next week in which a former fellow prisoner, Angela Hamilton, is accused of slashing her with a razor blade when they were both in Cornton Vale Prison in November 2011.
Hamilton was due to appear at a procedural hearing at Stirling Sheriff Court yesterday, at which a psychiatrist from Rampton would have given evidence about Riggi's fitness to testify. But the hearing was cancelled.
Her solicitor, Murray Aitken, said: "My hope is that the Crown will take the view that any further proceeding is unnecessary."
Sheriff Wyllie Robertson continued the case for a week, when Hamilton will be required to appear.
Riggi stabbed her children - eight-year-old twins Austin and Gianluca, and Cecilia, five - in 2010. She was originally charged with murder but later admitted culpable homicide on the grounds of diminished responsibility.