Progressive Draw 2 and Draw 4 Uno
If you look at the base rules of the game it ends as soon as a player has no cards in their hand. Which means that the second player would not have a chance to play the draw 2 in response to the first players card.

Also should be noted that if you are playing in a situation where you want to continue playing till everyone but the last person runs out of cards it would be the same. As soon as a player plays their last card they would be out of the game and not impacted by any cards.

uno rules


  Scoring: When a player no longer has any cards and the game ends, he/she receives points. All opponents’ cards are given to the winner and points are counted. All number cards are the same value as the number on the card (e.g. a 9 is 9 points). “Draw Two" – 20 Points, “Reverse" – 20 Points, “Skip" – 20 Points, “Wild" – 50 Points, and “Wild Draw Four" – 50 Points. The first player to attain 500 points wins the game.