Stock Retire

See: Buyback.

In order to retire stock, the company must first buy back the shares and then cancel them. Shares can not be reissued on the market, and are considered to have no financial value. They are null and void of ownership in the company.
Stock is repurchased from the money saved in the company's shareholder's equity line.

Why would a company retire stock? Like...why wouldn't they buy it back and just leave it in some drawer near the HR lady's coffee machine? Well, share existence in any form carries liability. If the shares exist, they get counted in the shares authorized totals, and sometimes, boards run out of room via shares which must underlie option grants, warrants, or other strategic equity dealings they must do to make their daily bread.