Bird rights
Bird rights (named for Larry Bird) are the exception that lets a team exceed the salary cap to re-sign its own free agent, up to his maximum salary. They're earned after three seasons without changing teams as a free agent.
While the player is unsigned, he occupies a cap hold of 150%–300% of his previous salary: lower-paid players carry the larger multipliers (250–300%) and higher-paid players the smaller ones (150–190%), so the hold approximates a realistic next contract.
See it live: pick any team and tap the numbers on its cap sheet.