According to The Work Buzz, "not eligible for rehire" is what a human resources department may report as a work reference if the employee in question was fired or otherwise left under unacceptable circumstances. While most companies do not elaborate on this, it can be a red flag.
Most companies refrain from giving out detailed information in a work reference, because negative information that affects someone's ability to get hired could lead to a lawsuit. However, most companies make it clear whether an employee would be eligible for rehire, and that information alone can imply whether or not the working relationship ended amicably.
