Settling in for a drink the other night at Jinja, the restaurant in Santa Fe, N.M., that Gene Hackman and his wife dined at and had invested in, a group of patrons decided to honor the couple by ordering a round of “Gene’s Mai-Tais” off the menu.

But in the days since Mr. Hackman, 95, and his wife, Betsy Arakawa, 65, were found dead on the floor of their home, the toasts and tributes have been freighted with a sense of bewilderment over the circumstances of their deaths.

Mr. Hackman was found dead near his cane in the mud room of their secluded home just outside the city, and Ms. Arakawa was found on the bathroom floor, next to a counter with pills scattered about. One dog was found dead in a nearby closet, while two others were roaming on the property, and data from Mr. Hackman’s pacemaker indicates he died nine days before the couple was discovered.

Now, Santa Fe, a city of 89,000 people that has drawn artists and cultural figures for decades, is grappling with a macabre mystery: How did two of their most famous residents die, and how could no one have known for so long?

“You can’t help feeling guilty that you didn’t call him,” said Stuart Ashman, a friend of Mr. Hackman’s who met him on a committee of the Georgia O’Keeffe Museum in Santa Fe in the late 1990s. “You sort of take for granted that your friends are where they are and everything is status quo.”

Among both those who knew Mr. Hackman and those who had never once seen him around town, theories about what might have happened were piling up.