33. What does renouncing a player mean?
As detailed in question number 30, free agents continue to be included in team salary. By renouncing a player, a team gives up its right until the following June 30 to use the Larry Bird, Early Bird, or Non-Bird exceptions (see question number 19) to re-sign that player. A renounced player no longer counts toward team salary, so teams use renouncement to gain additional cap room. After renouncing a player, the team is still permitted to re-sign that player, but they must either have enough cap room to fit the salary, or sign the player using the Minimum Salary exception. The exception to this is in the case of an Early Bird free agent who is coming off the second season of his rookie scale contract. Such players, when renounced, are treated as Non-Bird free agents. After renouncing a player, a team can still trade the player in a sign-and-trade agreement (see question number 76).
And....
76. Can a free agent be signed and immediately traded?
Under no circumstances can a team sign and then trade another team's free agent. But there is a rule that allows teams to re-sign their own free agents for trading purposes, called the sign-and-trade rule. Under the sign-and-trade rule, the player is re-signed and immediately traded to another team. This is done by adding a clause to the contract which stipulates that the contract is invalid if the player's rights are not traded to the specific team within 48 hours.
A sign-and-trade deal can be made even with players who have been renounced, but cannot be made when the player is signed using the Mid-Level, Bi-Annual or Disabled Player exceptions. Sign-and-trade contracts must be for three years or longer, but only the first season of the contract must be guaranteed. The three year minimum (even though the last two seasons may be non-guaranteed) ensures that the new team will not acquire Bird rights to the player any sooner than if they had signed him directly, because if they want to give him a new contract using Bird rights then they would have to waive him first, which resets the Bird clock.
So what does this mean? If you lose the bird rights to sign a guy and keep him on your team, shouldn't you also lose the bird rights to sign and trade him? But that's not addressed at all, it just says you can sign and trade renounced players.