In a competitive match, when a player quits, does the game look for a replacement?
Replacements are not allowed in competitive matches. There are several reasons why doing so is a bad idea:
The player who left might be able to return, if they just had a temporary internet problem or something. You don't want to have someone who is just about to get back in, but is blocked by a newcomer and is now unfairly saddled with the disconnection penalty.
Whoever replaces in will probably have a different rank than whoever left. How do you calculate the end-of-match rank changes? You can't use the old player because they're no longer a factor. You can't use the new player because that opens up ways for groups to grief the other team (such as having their highest-ranked guy leave and make way for hopefully a lower-ranked guy, so the other team wins less or loses more rank).
Chances are that the team with a missing player will be losing. Anyone who replaces in would be more likely to lose than win, through no fault of their own. Replacing would have a very negative stigma.
Akin to #2, whoever replaces in will probably not have the same skill level as whoever left. If replacements were allowed, this would result in teams bullying their worst teammate to leave in an attempt to get them replaced by a better player. Similar negative behaviour would occur if any sort of compensation were made for teams that have a leaver (e.g. a bot stands in, or the remaining players get a statistical boost to even things up).
Every competitive game does this, and it's purely a "competition" problem.
Let's imagine: The player quitting your game is bronze, the joining one is Silver. Now, not only teams are not balanced anymore, but the player that just joined is playing on an alredy started (and maybe almost finished game) granting him MMR (or points in OW), this means that if you're about to lose and someone quits and you join in instead of him, you just lost points without even playing a match.
If you instead don't give points for an already started game, every player that gets in one will just quit, because there is no reason for them to stay and play.
No, players are never replaced. This isn't actually a problem and here's why (I'll explicitly address the "problem" of it causing a lost match):
During an Overwatch competitive season match, if a player quits mid-match, my team will have to finish the match with one less player, which generally leads to a defeat.
Please recognize that teams that have a player who leaves (so, ignoring legitimate disconnects) are MUCH more likely to have lost even if the player didn't leave.
On occasion, someone is just upset early and leaves, but this is by far the exception and not the rule. Players that leave in that fashion will get suspended from competitive play very quickly.
It's very easy to look at your last 10 games and be like, "ah, well 3 of them were leaves, so I actually went 4-3 over 7 games". This would be very flawed reasoning and is simply a way of rationalizing to take the blame off yourself. I'm not saying this is what you're doing, I just want you to be aware of this red flag.
Finally, in the case of disconnects, this is just an unfortunate issue. Not much I can say about that. If you end up with a disproportionate amount of disconnects in a day, that's just rough luck. But in the long run, you should win just as many games as a result (unless it's your internet that is worse than the average player)