I really try my best to minimize the amount a character in my games gets sidelined. I know in games that I'm in as a player, there is nothing that kills engagement more than knowing I can't do anything because I'm dying or petrified.
That being said, I have a couple of ways I have handled this in my previous games.
1) I increase the number of saving throws. Rather than one save, it becomes two or three. Each failure creates a progressively bad outcome, but does not prevent the player from acting outright. For example, let's take hitting a player with the maze spell. First fail, they would feel dizzy and restricted in their movement as they feel the space around them become like molasses. The magic is beginning to pull them into the maze. Second fail, they have disadvantage on everything as they struggle to maintain their presence in the current world and resist the spell. Third fail, they get pulled through. In this example, the player has three opportunities to not only succeed the save (you may want to make it having them hit a certain number of success before hitting a certain number of failures) but the player can attempt to actively plan and strategize with the party to deal with it. Perhaps a dispel magic or greater restoration can be cast to prevent it or give an auto-success on one on their attempts.
2) Turn it into a mini-game. In the case of maze, give the player an opportunity to get out. Just because they've been bamf'ed to somewhere else, does not mean they don't have anything to do. They may have their own threats to deal with in the maze. One time, for an in-person group, I gave one such player one of those celtic puzzles that you need to figure out a way to break it apart. If she could take it apart, the effect would end. Over internet games are a bit harder to do something similar. But at the very least, I would allow a player to in some way still be able to act and communicate with the team, even if minimally. Another example, perhaps that player that has been dropped and is dying is still able to see and communicate. They can crawl maybe 5' a round, and they can still talk. Maybe because they are watching their friends fight, the downed player can shout warnings, which could be treated as a ranged Help action (only available when dying or down but stable). That way the player still has a reason to engage AND feels like they are contributing.