Chances are good that the hose you speak of should be connected to the vacuum port of your petcock. Without this hose connected, the petcock must be set to PRIME or you won't get any fuel flow at all.
However, if it is set to PRIME this means if your carb float valve is stuck, gasoline will leak into the airbox and may end up in your engine oil which can result in severe engine damage.
You need to fix the carb float and reconnect the hose and make sure your oil did not get contaminated with fuel. If in doubt, it is highly recommended to change oil and filter. This is much cheaper than rebuilding your engine.