David Perry, a family spokesman, said her family were "stunned" and were enduring a "nightmare".
The hospital and sheriff's department conducted a search of the premises and Ms Spalding's friends and relatives spent days scouring the streets of the California city with flyers.
They said they were "under the assumption San Francisco General had been searched."
Mr Perry said: "Lynne Spalding died alone, in the stairwell, at one of the finest medical institutions in this country.
"I hear that the San Francisco Sheriff's Department initiated a search. Well, evidently it wasn't a very good one. I think there are a lot of questions to be asked."
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Emma Jesson brings you Sunday night's forecast
Wet and windy spells, interspersed with drier interludes this week. Breezy with wintry showers, variable temperatures and a weather warning
Mostly cloudy, some bright spells, rain on and off and blustery. Milder temperatures than on Saturday