If my role (let's say the Scientist) has 4 cards of the same color but was not able to get to a research station. And, let's say a different player (the Operations guy) lands on the same city as the Scientist and in his last action he builds a research facility in that city. The Scientist is now in the city with the research facility, but just as it is now the Scientist's turn, there is only 1 card remaining in the player deck.
Did the team run out of time?
Technically, as the player's turn begins with actions, the Scientist can cure the last disease before having to draw the 2 cards which would result in the game ending--except that the cure had been placed on the board ending the game in a win.
So, can a turn begin when there is only 1 card in the player deck, or must there be 2?