There are at least two benefits that will be associated with this.
First, productivity will presumably rise. In order to make the same amount of product with 10% fewer workers, you will need each worker to be more productive. This will force the firm to become more efficient.
Second, profits should increase. If you are making the same amount of product with 10% fewer workers, you should get the same revenue at a lower cost. Increased profits will make your firm more attractive to investors if that is something that you are interested in.
Thus, cutting employees can have beneficial results other than those directly connected to payroll.