The scene played out for years. Twice a week, in the late afternoon, above the Shun Lee Chinese restaurant on the Upper West Side of Manhattan, a creaky elevator would open, and out would step an elderly man. Thin as a rail, with a sparse mustache, he would sometimes have little idea about where or who he was. A pair of security doors would buzz unlocked once surveillance cameras identified him as the artist Peter Max.

Inside, he would see painters — some of them recruited off the street and paid minimum wage — churning out art in the Max aesthetic: cheery, polychrome, wide-brushstroke kaleidoscopes on canvas. Mr. Max would be instructed to hold out his hand, and for hours, he would sign the art as if it were his own, grasping a brush and scrawling Max. The arrangement, which continued until earlier this year, was described to The New York Times by seven people who witnessed it.

In the 1960s and 1970s, Mr. Max was a countercultural icon, a rare painter to achieve name recognition in the mainstream. His psychedelic renderings could be found on the cover of Time, the White House lawn and even a postage stamp. But several years ago, he received a diagnosis of symptoms related to Alzheimer’s, and he now suffers from advanced dementia. Mr. Max, 81, hasn’t painted seriously in four years, according to nine people with direct knowledge of his condition. He doesn’t know what year it is, and he spends most afternoons curled up in a red velvet lounger in his apartment, looking out at the Hudson River.

For some people, Mr. Max’s decline spelled opportunity. His estranged son, Adam, and three business associates took over Mr. Max’s studio, drastically increasing production for a never-ending series of art auctions on cruise ships, even as the artist himself could hardly paint.