[HeadOn]

Matthew 19:9 - And I say unto you, Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery.

Believers can (but do not have to) divorce a cheating spouse.

1 Corinthians 7:15 - But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace.

If a Christian is married to an unsaved person who abandons them, they may (but do not have to) divorce that person.

[Campion]

It says "fornication," not "adultery". The "exception" is for marriages that were not valid in the first place, e.g., within the prohibited degree of blood relationship in the Mosaic Law.

If a Christian is married to an unsaved person who abandons them

A marriage between a Christian and an unbaptized person is not a sacrament, and can be dissolved. Catholic marriage law covers this under the terms "Pauline privilege" and "Petrine privilege".