It really depends on the case. Some mentioned above are a case of a team going from their backup TO their starter, which doesn't really count. Lyon was never actually Florida's starter, he began the playoffs in net because Bob and Knight were both out, and he was incredible in their stead, and even though Bob had healed up, it was wise to wait until Lyon inevitably cooled off, which they did. Grubauer was not Washington's starter, he was just more in form at the end of the regular season, and similar deal, he cooled off, Holtby got in. Pittsburgh tried to switch back to Fleury in 2016, but he was just too rusty, so they put Murray back in.
I truly believe Carolina either pulled Andersen because there's something going on mentally over Claude Lemieux or he was concussed in Game 3 on the GI disallowed goal. Evidence? He's not even been on the bench, he's not practicing with the team and they even called up another goalie. The truth will come out after this final ends one way or the other. Bussi has done fine since going in, and if he gets the last 3 wins, he'll have made a meaningful contribution in his starter's stead, and Brind'Amour will have been proven correct that both would be needed.