Here is some stuff I have found on how it works in the NBA.
Can be read at the following link.
http://members.cox.net/lmcoon/salarycap.htm
DISABLED PLAYER EXCEPTION -- This exception allows a team which is over the cap to acquire a replacement for a disabled player who will be out for the remainder of that season (if the player is disabled between July 1 and November 30) or the following season (if the player is disabled after November 30). This exception can also be granted in the event of a player's death. This exception can only be used to acquire one player. The maximum salary for the replacement player is 50% of the injured player's salary, or the average salary, whichever is less (see question number 24 for the definition of "average salary"). Approval from the league (based on a determination by an NBA-designated physician) is required for this exception to be used. This exception can be used to sign a free agent, or to create room to accept a salary in trade. When used for trade, the team may acquire a player whose salary (including any trade bonus) is up to 100% of this exception plus $100,000 (not 125%). Also see question number 20 for more information on the availability and use of this exception.
If a player is disabled between July 1 and November 30, the team must acquire the replacement player within 45 days. If the player is disabled between December 1 and June 30, then the team has until October 1 to sign a replacement. If the disabled player comes back sooner than expected, then he may be activated immediately, and the replacement player is not affected. However, if the disabled player comes back before the exception is used, then the exception is lost.
Teams sometimes have had difficulty getting the NBA to approve an injury exception. For example, Danny Manning tore an ACL toward the end of the 1997-98 season, yet the NBA did not approve the Suns for this exception. More recently, the Magic did not receive this exception in 2003 for Grant Hill. However, this exception was granted in the 1999 offseason to San Antonio, so they could replace Sean Elliott, who was disabled due to kidney problems. This exception was also granted to Charlotte soon after Bobby Phills was killed.
Don't confuse this exception with the salary cap relief teams can apply for a year after losing a player to a career-ending injury or death (see question number 54). This exception allows a team to acquire a replacement player. The salary cap relief removes a contract from the books.