The term "fictional unemployment" is not a commonly used term in economics, and it is not recognized as a separate category of unemployment by most economists. It is likely that your professor meant to say "frictional unemployment" instead of "fictional unemployment."
Frictional unemployment is a type of unemployment that occurs when workers are in between jobs, either because they are searching for a new job or because they have left their previous job and have not yet started their new job. It is a natural part of the labor market and is not considered a problem as long as it is not too high.
The example you provided about a subsidy or incentive leading to unemployment is not typically referred to as "fictional unemployment." Instead, it is usually referred to as "incentive unemployment" or "disincentive to work." This occurs when government policies or programs provide benefits or subsidies that discourage people from working, which can lead to higher unemployment rates.