Off the top of my head, Vegas in 2017-18 comes to mind. Fleury and Subban both missed nearly a month of games. Fleury himself was gone for nearly two months.
Fleury and Subban combined to start 65 games that season, and started all but 1 game after December 10, so not sure if they really fit the criteria, but, they did lose both their starter and backup for 13 games in October/November and the team somehow still went 7-5-1, despite allowing 43 goals on 369 shots (0.883 SV%).
So, the examples seem to be Ottawa, who needed Hammond to go 20-1-2, and Vegas, in their inaugural season when everything just went their way. Not really scenarios that most teams can replicate, which is pretty much my point. Expecting teams to overcome losing both their starter and backup is extremely unrealistic, and even more so in the playoffs.