If you sold your interest in a business back to the corporation and later bought back in, the corporation would simply issue new shares to reflect the new purchase.

In the ideal world, when someone sells his or her shares, they turn the stock certificates representing those shares back to the corporation to be canceled. You wouldn’t get the exact same piece of paper (stock certificate) handed back to you. Like getting divorced and remarried to the same person, your new anniversary is the date of the remarriage, not the date of the initial wedding.