If one of the separated parents is unemployed all year with no income, can the other parent claim all dependents?

there is a court ordered agreement from 10 years ago that states that each parent claims one child. She has $0 income to report this year and will not be filling a tax return. There was only one parent that provided for the children and she will not be claiming a child. Is it correct that the other parent can then claim both as dependents?