Kind of...
You can resign any player you have had for I believe 3 years for a figure over the cap subject to league maximums (Bird Rights). To retain Bird Rights, you take a figurative "hit" on your cap at 1.5 times the guy's salary. I'm not sure when or if you have to formally rescind Bird Rights, but if Player X made $10 million last year, the team would have $15 million less in room until they rescind the rights.
If you have a player for 3 years, and you rescind, and then sign him to a smaller contract, you retain their Bird Rights upon the expiration of the contract. In theory, yes, we could rescind Lee's Bird Rights, sign him to a small one year deal with a *wink**wink* ::nudge:: ::nudge:: guarantee he will get paid the next year...