MEMPHIS — When one of Martha Jane Pierce’s sons peeled back the white sock that had been covering his 82-year-old mother’s right foot for a month, he discovered rotting flesh.

“It looked like a piece of black charcoal” and smelled “like death,” her daughter Cindy Hatfield later testified. After Mrs. Pierce, a patient at a nursing home in Memphis, was transferred to a hospital, a surgeon had to amputate much of her leg.

One explanation for Mrs. Pierce’s lackluster care in 2009, according to financial records and testimony in a lawsuit brought by the Pierce family, is that the nursing home, Allenbrooke Nursing and Rehabilitation Center, appeared to have been severely underfunded at the time, with a $2 million deficit on its books and a scarcity of nurses and aides. “Sometimes we’d be short of diapers, sheets, linens,” one nurse testified.

That same year, $2.8 million of the facility’s $12 million in operating expenses went to a constellation of corporations controlled by two Long Island accountants who, court records show, owned Allenbrooke and 32 other nursing homes. The homes paid the men’s other companies to provide physical therapy, management, drugs and other services, from which the owners reaped profits.