“The Killing” 8 p.m., AMC

Even in the depths of a Philippine jungle, death had a way of finding Veena Sud.

It was there that Sud, the show runner of the praised and polarizing AMC crime drama “The Killing,” had traveled last summer after finishing work on its second season, to escape from civilization and the demands of her job. But one morning at 4 a.m., she got a phone call informing her that “The Killing” had been canceled.

Still, Sud felt certain her show had life left in it, a mind-set she attributed to the eternal optimism of television producers.

“We always believe we’re coming back,” she said in a telephone interview from Vancouver, British Columbia, where “The Killing” is produced. “We’re going to believe it 10 years later, and it’s not coming back. But I believed it.”

Later that year, Sud found herself in a less exotic location — a McDonald’s drive-through — when she got another call: “The Killing” had been resurrected for a third season.

When it has its season premiere on AMC tonight, “The Killing,” a serial narrative about Sarah Linden and Stephen Holder, two detectives (played by Mireille Enos and Joel Kinnaman) investigating a murder in dismal, rain-drenched Seattle, it will be recovering from a combination of seemingly insurmountable events.

Despite a first year in which “The Killing” (adapted from the Danish series “Forbrydelsen”) drew positive reviews and a loyal audience, its following eroded after the season finale failed to solve its central mystery — the murder of the teenager Rosie Larsen — and outrage erupted among critics and rank-and-file viewers alike. When AMC canceled the show, the most faithful fans had to believe it was dead and buried.

Now as it returns, the producers of “The Killing” are hoping this third season will be a chance at a clean slate. For them, this is an opportunity to build on its strengths, right the wrongs of its past and, with new cast members and a new story line, offer a different take on a familiar series.

“We believed that the show had merits that the audience recognized in Season 1,” said David Madden, the president of Fox Television Studios, which produces the show. “If we could get a third shot at the plate, we could get the audience back. And we could get them back for good.” That “The Killing” must once again make its case — after a 2011 debut that Alessandra Stanley of The New York Times described as “bleak and oppressive” but “so well told that it’s almost heartening” — has much to do with that first year, when, Madden said, “we had a very rocky season in terms of the perception of the show.”

Although the solution to Rosie Larsen’s killing was provided the next year, many audience members did not stick around to find out: ratings for “The Killing” declined, to 1.7 million viewers, from about 2.3 million viewers for new episodes in Season 1, and this concerned AMC. As the AMC president, Charlie Collier, put it: “We saw some metrics in the second quarter that said the noncore fans were not there in the way they were in Season 1, so we had some decisions to make.”

Collier acknowledged that the backlash to the Season 1 finale “was a contributor” to this slump, adding: “It’s been well-documented, a lot of this. We never intended to mislead anybody.”

When the cancellation of “The Killing” was announced last July, AMC said it was a “difficult decision,” and praised its cast and crew. The Fox studio went a step further, saying it would “proceed to try to find another home for the show.”

Madden said the studio was not yet ready to give up on a series that had two rising stars in Enos (whose coming films include “World War Z”) and Kinnaman (who is playing the lead role in a remake of “RoboCop”), and that at one point had a proven ability to draw viewers.

When Enos heard rumors that “The Killing” was returning to AMC, before it was made official in January, she said, “I texted Veena, and I was like, ‘Whaaaaat?’ And she texted back and said, ‘Crazy world, huh?’”

Sud was prepared to pitch AMC and Fox on her plan for the third season — one that she said she viewed “almost like a pilot” for a new show — that would revisit the lives of Linden and Holder a year after the Rosie Larsen case and after their partnership has dissolved. Drawing on themes from documentaries like “Streetwise” and the photographs of Mary Ellen Mark, Sud wove in a second plot about teenage runaways living on the streets of Seattle. A third story line focuses on a mysterious death-row inmate named Ray Seward, played by Peter Sarsgaard, a star of films like “Boys Don’t Cry” and “Kinsey.”

Unlike the first two seasons of “The Killing,” Season 3 also promises an overarching mystery that will be resolved in a single year. But Sud said this was a development that occurred organically and not at the demands of AMC or Fox.

The story “definitely could be told” in 12 hours, she said. “It would be very tight, economical, but still allow for really momentous storytelling.”