An employee gives Form 637 to their U.S. employer to claim an exemption from U.S. income tax withholding on wages earned abroad. The employer is not part of the qualifying process. They are only following the employee's request not to withhold taxes on the employe's wages.
When the employee gives Form 637 to their employer they are anticipating that they will meet either the physical presence test or bonified presence residence test to qualify for the Foreign Earned Income Exclusion FEIE. It is up to the employee to meet the requirements to claim the FEIE.
Based on the information in your question the employee would not qualify for the FEIE as they only had 320 qualifying days. Therefore, all of the employee's wages would subject to income tax.
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