Reject worker after match
In the standard model, all workers have the same productivity. So if J &lt; 0, your expected value of a vacancy would also be negative. That the reason why, once a match is made, the only variable to be set is the wage. In the real world, they have to deal with different expected productivities.

Pissarides 94 distinguished between two kinds of applicants (but in this case, the firm is passive in the decisions).