Big Pot: 3 ways on river, Player A checks, Player B open folds, Player C left to act on Button

There's no rule against folding your hand when action is on you. That's why nobody said anything about it.

I wouldn't open fold either. Years ago, I saw a hand where a new player tabled a hand and the villain folded. The thing was that the new player didn't realize that 3 pair was not a legal hand. The 3rd pair was 22 and as such, the new player had 2 pair on the board with a 2 kicker. It was impossible for the villain to lose.

That said, an experienced player will often just fold when there is almost no chance to have a winning hand to speed the game up.

this is the TDA rule:

So it's in a gray area I guess. It's not technically against the rules, but it is "subject to penalty" so it's at least frowned upon, and the situation you describe is probably one of the ones they would most want to discourage. Folding out of turn is probably more the part of that compound rule which one might get penalized for.

Having said that, there is no specific rule it violates, especially in a cash game, and most players don't care and know it helps speed the game up in many situations, usually when more players are still in it, or when it is heads up.

Folding in turn (facing no bets) doesn't happen much. I don't like it when the player stays at the table because like in this hand, it gives an advantage to the players still left to bet.

But typically when a player folds in turn they go to the bathroom or leave the table to make a phone call. That way they don't have to pee in their pants at the table.

Its when a player folds out of turn and gets up to go to the bathroom that is problematic. But really it just gives an advantage to all players in the hand who can still bet.

I can say in this specific hand, the pro stayed at the table. He did not get up (Player B)

Cash game - who cares. Tournament - I would prefer it not be allowed. I don't have a good reason except for "feels".

It's called folding to a check and is not allowed, but often not enforced in tournaments and basically never enforced in cash games. It changes the dynamic and is disrespectful IMHO.

It's mostly something I see in smaller cash games.

If you are one of the other players, you should care, because it really messes up the action, giving an advantage to the player in position.
I have lost at least one pot that I almost certainly would have won if someone else hadn't pulled that crap.

Oh, I understand why you shouldn't do it and never do it myself. But I have a hard time caring in a cash game, whereas in a tourney I'll point it out. May not be logical, but like I said, feels.

Very bad etiquette in general, as it gives Player C an unfair advantage. In some cash games floor would be called after the hand is completed.

Situationally - it might not matter as much based on the hand history, and players knowing each other, etc.

Minor trangressions before there isn't much money in the pot typically isn't a big deal, especially pre-flop or the flop in large multiway pot. The folding out of turn pre-flop after seeing your hand is not AA because you need to get up soon situation is mostly acceptable as long as people don't do it too often. Cash games where the rules are too strict and that don't allow any wiggle room, aren't going to attract a lot of players everyone wants in the game.

In bigger and more serious games, experienced players are going to be a lot more careful not to do this.