The term for a corporation's own stock that has been repurchased and not retired is treasury stock.
A company creates treasury stock when it buys back shares that were previously issued and fully paid. The shares remain legally associated with the issuing company, but they are no longer counted as outstanding shares while held in treasury. Companies may repurchase shares to return cash to investors, offset employee stock compensation, signal that management believes the shares are undervalued, or reduce takeover risk.
Treasury stock is reported within shareholders' equity, commonly as a contra-equity balance that reduces total equity. It is not treated as an asset, because a company cannot hold an ownership claim against itself. Treasury shares generally have no voting rights and do not receive dividends while the company holds them.
The key distinction is between holding and retiring shares. Held shares can later be reissued, whereas retired shares are canceled. “Common stock” describes the original class of shares, not their repurchased status, and retained earnings is an equity account rather than the name for the shares themselves.