A Washington state couple are on the run after authorities found their emaciated 16-year-old son weighing just 54lbs (24.5kg) last year.

Anthony Foxworth, 45, and his wife Mary Foxworth, 42, have jumped bail after pleading guilty to a criminal mistreatment charge in Lewis County Superior Court last month.

But earlier this week the pair failed to show up for their sentencing, leading presiding Superior Court judge Joely O'Rourke to issue a warrant their arrests.

Police say the couple were last seen in Grand Mound, to the north-west of the state, at a gas station with their green and silver 1998 Chevrolet Suburban.

Prosecutor's say they had planned to recommend a sentence of 51 months each, or more than four years in prison, for Foxworth and his wife.

The couple were accused of committing "great bodily harm" to one of their children between January 2007 and January 2016.

Police first became aware of the child after the Foxworths went to see a doctor in January 2016 with their son, who has not been named, complaining that he had not eaten for three weeks.

The teenager was eventually taken to Mary Bridge Children's Hospital for treatment where medical staff found the skeletal child was unable to talk, stand unaided, and had never been taught to use a toilet.

He had a number of bald spots and 24 of his teeth needed dental work. Doctors at first thought the teenager was between 8 and 10 years old.

A year later, the boy has gained 93 pounds and grown 3.5 inches while in the care of a foster family, reported local broadcaster KCPQ.