Pierce opted out and signed a new contract. He didn't restructure his deal. Under the old CBA, Garnett couldn't re-structure his deal, as far as I can tell. I'm not sure about the new one. I have not seen any clear reference as to whether or not the "renegotiate and extend" provision made it into the new CBA, but if it did, KG could have renegotiated his salary downward this year if he extended his contract. I'm not sure KG signed to more years.
However, the Celtics are so far over the cap that even if KG could have given back half his salary, it wouldn't free up space to do much to improve the team's center situation. Maybe the Celtics end up with Kwame Brown instead of Chris Wilcox, if that can be considered an improvement.