The chain of events that led to the death of a black woman in a South Carolina jail last July began with a desperate bid to save her life from alcoholism.

When details of Joyce Curnell’s death at the Charleston County jail surfaced this week in court documents, they drew broad condemnation. Ms. Curnell, 50, had been arrested just a day earlier while seeking care at a hospital for a stomach illness.

Lawyers working for the woman’s family, which is preparing a lawsuit, said she could have been saved if she had been given adequate medical care.

Others wondered how officers had come to arrest Ms. Curnell, after she checked into an emergency room, on a bench warrant stemming from about $1,150 in fines she had failed to pay over the theft of some candy and beer in 2011.