In the DMP family of labor models, we typically have $V$ denoting a vacancy and $J$ denoting the value of a job. $V$ typically becomes 0 through free entry.
Say a firm get matched with a worker of value $J_i$ and could reject him, to search again. In order to do so, it would need to hold that $V > J_i$. But as (through free entry) $V = 0$, that would only be the case if the worker has zero value to the firm.
However, in the real world, we see firms rejecting applicants and searching for new applicants. How do DMP models achieve to generate this observation?