Warning -
@Ben8257 style lengthy response below.
TLDR option available...
Roberts Rules of Poker (RROP) has a couple of relevant rules on this:
"If everyone checks (or is all-in) on the final betting round, the player who acted first is the first to show the hand. If there is wagering on the final betting round, the last player to take aggressive action by a bet or raise is the first to show the hand. In order to speed up the game, a player holding a probable winner is encouraged to show the hand without delay. If there are one or more side pots (because someone is all-in), players are asked to aid in determining the pot winner by not showing their cards until a pot they are in is being settled. A player may opt to throw his hand away after all the betting for the deal is over, rather than compete to win the pot. However, the other players do not lose the right to request the hand be shown if he does so."
"Any player who has been dealt in may request to see any hand that was eligible to participate in the showdown, even if the opponent's hand or the winning hand has been mucked. However, this is a privilege that may be revoked if abused. If a player other than the pot winner asks to see a hand that has been folded, that hand is dead. If the winning player asks to see a losing player’s hand, both hands are live, and the best hand wins."
Generally this second rule is infrequently invoked, as some consider it bad form (even though it is completely legal).
Also from RROP:
"Cards thrown into the muck may be ruled dead. However, a hand that is clearly identifiable may be retrieved and ruled live at management’s discretion if doing so is in the best interest of the game. An extra effort should be made to rule a hand retrievable if it was folded as a result of incorrect information given to the player"
So a player MAY still be able to win the pot after mucking.
Tournament Directors Association (TDA) has a couple of rules related to this:
" If the house does not have a mucking line or forward motion rule at showdown, pushing non-tabled cards forward face down does not automatically kill them; a player may change his mind and table his cards if they remain 100% identifiable. However, the cards are at risk of being killed by the dealer when he pushes them into the muckpile."
"All cards will be tabled without delay once a player is all-in and all betting action by all other players in the hand is complete."
" In a non all-in showdown, if cards are not spontaneously tabled, the TD may enforce an order of show. The last aggressive player on the final betting round (final street) must table first. If there was no bet on the final street, then the player who would be first to act in a betting round must table first (i.e. first seat left of the button in flop games, high hand showing in stud, low hand showing in razz, etc.). Except where house policy requires a hand to be tabled during the order of show, a player may elect to muck his hand face down"
"Players not still in possession of their cards at showdown, or who have mucked face down without tabling their cards, lose any rights or privileges they may have to ask to see any hand.
TLDR: The answer to your question is - Maybe...
In general,
- Cards should be shown in order (last aggressive player first) except in all-in tournament scenario, where all cards must be turned over immediately.
- A player can abandon his claim to a pot by mucking.
- The winning player (actually any player still in the hand) can ask to see the other player's cards even if mucked.
- Asking to do so if a player doesn't want to show his cards may be considered bad form, and also exposes the "winner" to actually losing (cards speak).
- If the cards cannot be readily identified from the muck, then cards are dead and move on.