Is it possible to win in MTG when you don't have enough cards in your library to complete your draw phase?
Sure it's possible, but you'd need to win at instant speed. An example: your opponent has 3 life left, and you're holding a Lightning Bolt. Then when the Howling Mine triggers but before it resolves (which would kill you), you point Lightning Bolt at him and kill him. You could also do this on your upkeep, before the draw phase.
Or are you asking why the rules says &quot;he or she draws the remaining cards, and then loses the game the next time a player would receive priority&quot; as opposed to simply &quot;he or she loses the game the next time a player would receive priority&quot;? That would be because it's possible to not lose the game even though you are supposed to lose. For example, if you are controlling Platinum Angel, then you don't lose for trying to draw from an empty library. In that case it makes sense for you to draw the remaining cards anyway.