Jamieson, Fausset and Brown on 1 Corinthians 7:13

13. the woman--a believer.

let her not leave him--"her husband," instead of "him," is the reading of the oldest manuscripts The Greek for "leave" is the same as in 1Co 7:12, "put away"; translate, "Let her not put away [that is, part with] her husband." The wife had the power of effecting a divorce by Greek and Roman law.