How does Mrs Coulter die in the series of books " His Dark Materials"by Phillip Pullman??

Answer 1

In The Amber Spyglass:

She falls into an abyss:

"Mrs. Coulter enters the Clouded Mountain, citadel of the Authority, where she meets the Regent Metatron. Mrs. Coulter manipulates Metatron by offering him Lord Asriel's life. This is similar to the means by which Lyra had tricked Iofur Raknison, Iorek's rival for kingship of the bears; in that Lyra had used Iofur's desire to become human to trick him, much as her mother uses Metatron's desire to experience sensual pleasure to confuse him. Mrs. Coulter betrays Metatron to Lord Asriel, on the grounds that Lyra is precious to both of them. All three tumble into an abyss.
Will and Lyra enter the world of the mulefa. They grab their dæmons immediately before doing so; the dæmons run off again."

But does she die? Pullman doesn't say.

Answer 2

She and Lord Asriel, along with their daemons, are fighting Metatron by the edge of the Abyss (the rent between all the worlds). In order to destroy him, they jump on Metatron and they all fall into the cleft. This is a great sacrifice, because it means that they won't pass through the world of the dead and become part of all matter, the way that everyone else will now that window has been opened.