When you cannot draw a card at the beginning of your turn due to having no cards in your deck is called a deck out. You lose when this happens.
If you have 1 card left in your deck, you can still draw that and complete your turn. But just realise that if you do not win the game on that turn you will automatically lose next turn as you have no cards to draw (unless you use effects or trainers to put cards into your deck during your last turn).