The primary source I read was about Griggs, a chimney sweeper and small child who escorted him.The fire had been lighted as early as 2 o'clock the same morning, and was burning on the arrival of Griggs and his little boy at eight. Griggs had no sooner extinguished the fire than he suffered the child to go down the chimney; and the outcome, as might be expected, was his almost immediate death, in a state, no doubt, of overwhelming pain. The chimney was of the narrowest description, and must have reserved heat enough to have prevented the child's return to the top, Soon after his fall, the master, who remained on the top, was worried that something had happened, and therefore wanted him to come up; the answer of the boy was, "I cannot come up, master, I must die here." An alarm was given in the brew house immediately that he had stuck in the chimney, and a bricklayer at work near the spot attended, and after knocking down part of the brickwork of the chimney, just above the fireplace, made a hole sufficiently large to draw him through. A doctor attended, but all efforts to bring back life were unsuccessful. On inspecting the body, various burns appeared; the fleshy part of the legs and a great part of the feet more particularly were injured; those parts too by which climbing boys effectually ascend or descend chimneys, viz. the elbows and knees, seemed burnt to the bone, from which it must be evident that the unhappy sufferer made some attempts to return as soon as the horrors of his situation became apparent.

questions: Was this death preventable?
No, this death was not preventable because both ways the poor child was trapped. He could neither climb out of the chimney nor could he stay back and face immediate death. He had burns all over his body, and couldn't have even tried to come up and make his way through.

There is another possibility here. What if the child had not been asked to go down into the chimney?