I'm not 100% sure on this, but I believe they can... However, since the NBA features a soft cap (meaning you can go over the cap, but you have to pay extra to the league), no one is ever asked to.
I think Richard Jefferson took a paycut to stay with the Spurs a couple years ago. It can happen, just very rare.
Edit, nevermind. He apparently declined a player option and re-signed for less.