If you renounce a player, you can still sign that player using cap space or whatever exception you have available, including the veteran's minimum exception.
Renouncing everyone and using cap space means you lose the full MLE and the biannual exception, so it only makes sense to renounce players if you are going to sign a player to a contract larger than the MLE. If, for example, you re-sign KG and renounce everyone else so you have just enough room to sign one free agent, you are effectively trading whoever you could have brought back among Bass, Green, and Allen (and Krstic, I suppose) plus whatever you could have gotten for $5m/year with the MLE for that one player.