How and why does Miss Havisham die in Great Expectations?

Miss Havisham dies because she goes too close to her fireplace in her distraught condition after asking Pip to forgive her. The material of her old wedding dress, which she has worn for decades, is so rotted that it immediately goes up into flames.

In Chapter XLIX, Pip arrives at Satis House after having been given a note from Miss Havisham when he was previously at the office of Mr. Jaggers. He shows the note to an older woman he has seen before who guides him into a larger room that Miss Havisham usually occupies. She tells Pip that "to show you that I am not all stone" she wishes to help out with his friend, about whom Pip has petitioned her aid on his previous visit. When she inquires about the details, Pip explains about the secret partnership he has made on behalf of Herbert, but he needs funds of nine hundred pounds. 

"If I give you the money for this purpose will you keep my secret as you have kept your own?"

Pip promises to do so. Then, Miss Havisham asks if there is nothing that she can do for Pip himself. After he reads the note instructing Mr. Jaggers to release the money to Pip, her hand shakes as she takes the pencil from its chain attachment to the pad on which she has written. She tells Pip,

"My name is on the first leaf. If you can ever write under my name 'I forgive her' though ever so long after my broken heart is dust--pray do it."

"Oh, Miss Havisham,...I can do it now. I want forgiveness and direction far too much to be bitter with you."

Overcome with emotion, Miss Havisham drops to her knees before Pip, crying in despair, "What have I done! What have I done!" as she realizes the extent of her cruelty to young Pip in conditioning Estella to be heartless. For, when Pip visited the other day, Miss Havisham saw herself in Pip as he opened his heart to Estella, and she knew then his terrible heartbreak, emotions so much like her own so long ago. Pip sees an earnest compassion now in her new feelings for him, and he is deeply touched.

Pip repeats that he forgives her and signs his name as she requests. Then, he asks about Estella's past and who her mother is. When he learns all that Miss Havisham knows, Pip makes his departure. After reaching the courtyard, Pip hesitates whether to call the woman to open the gate or to first check to be sure that Miss Havisham is all right. He decides to go back to her room and discovers that she has pulled her chair too close to the fire. She runs shrieking, "with a whirl of fire blazing all about her" and soaring above her head. Quickly, Pip removes his great coat and smothers the flames by enclosing her within it. He puts her down on the floor and pulls off the tablecloth to further smother the flames.

A physician is summoned and he says that Miss Havisham's main danger is in the nervous shock she has received. As Pip leaves, she repeats over and over the three sentences about what she has done, asking to be forgiven, and requesting Pip to sign his name. It is not long after this injury that Miss Havisham dies.