What happens if the Draw pile runs out of cards before anyone wins the round?
If no player is out of cards by the time the Draw pile is depleted, the Discard pile is reshuffled and play continues. Additionally, if the last card played in a round is a Draw One, Draw Five, Wild Draw Two, or Wild Draw Color card, the next player must still draw the required cards, which are then counted when points are totaled.
From the official Mattel GDR44 Uno Flip Card Game manual, page 1
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