The player is no longer involved in that round. The above rule is known as late surrender. In some casinos players can surrender before the dealer checks his cards for a blackjack. When the dealer's upcard is an ace, the dealer will ask players if they want to make the insurance wager. It is a side bet in which players are betting that the dealer's hole card will be a ten-value card.
Players can make an insurance bet equal to one half of the initial bet made on the hand.
To make the insurance bet you simply place your chips on the insurance line, which is located right above the player betting box. You win your insurance bet if the dealer has a ten-value card in the hole. A winning insurance bet pays off at 2 to 1 odds. Taking even money yields the same result as making an insurance bet on your blackjack hand. Unlike players, the dealer in blackjack has no playing option.