If an unbelieving spouse leaves, can the believing spouse remarry (1 Corinthians 7:15)?

Fortunately the church addresses this directly. The verse in the Douay-Rheims says, but if the unbeliever departs, let him depart, for a brother or sister is not under servitude in such cases. The word depart is in the Greek middle voice, indicating the unbeliever separates himself from the marriage on his own decision; nobody coaxes him, and that is part of what makes it valid. The phrase not under servitude, or not under bondage, is a perfect passive placed forward for emphasis, meaning the condition of release from being bound to the marriage arrived as soon as the unbeliever separated and continues into the future. Then canon law, canon 1146 of the 1983 code, says the baptized party has the right to contract a new marriage with a Catholic party if the non-baptized party departs without just cause. This is called the Pauline privilege: the believing Catholic has the right to remarry once the unbelieving spouse has left. So that is your answer.