Burn cards are cards dealt face down and discarded from the top of the deck, used to prevent marked cards from being identified.
In the case of a boxed (face-up) card appearing in the initial deal, the burn serves as its replacement. In this situation, the deal is completed and the player with a boxed card is dealt an extra card and the boxed card is placed on the top of the deck face up as the next burn card. It is turned face down when it is eventually burned.
In lower limit games with people you trust, burns are not really needed.
Boxed cards therefore stay live unless and until the player who received it calls a misdeal. They are the only ones who can call a misdeal and they have roughly 3 seconds to decide. If they decide to keep it, the game continues as if a mistake had not occured.
If the player calls a misdeal, the dealer must collect all the cards, shuffle up and start again. Two consecutive misdeals and they lose the deal and must post a dead big blind in the following hand as their punishment.