Cynthia D’Aprix Sweeney, a former marketing copywriter in Los Angeles, dreamed for years of becoming a novelist but never had any illusions about earning a living from it. Her goal in writing her first novel, “The Nest,” which she tackled in her early 50s, was merely to finish it.

In a whirlwind week as publishers read the manuscript last December, HarperCollins’s Ecco editorial director Megan Lynch made a pre-emptive offer to publish the novel for at least $1 million. “I never imagined people would respond that way in a million...