Trades
The disabled player exception is a one-time lifeline for a team that loses a player to a season-ending injury. The league grants room to sign or trade for one replacement, worth the smaller of the mid-level or half the hurt player's salary.
It only buys one player on a one-year deal, and it doesn't clear the injured contract off the books. It is a patch for the rotation, not a refund.
See it live: pick any team and tap the numbers on its cap sheet.