It always depends if you must draw cards or not.
A typical full hand is 5 cards. You can have to draw extra card with cards like
emerald sword or have to draw less than 5 card with cards like
Mask of the murderer.
The point is not drawing or not drawing, but drawing enough cards to fill your hand.
When you draw a card and have only 4 cards in hand, you lose.
When you can't draw and have 5 cards in hand, you're safe.
Another point is that you draw at the beginning of the turn.
In your case, when Zil boss draw in turn 5 his last card, if he has 5 cards in hand, he is safe. He can play turn 6.
Both part can't draw enough card in turn 6, at the end, the two lose for deck out. In this case the victory is decided at better score.
You lose.