Snowblower Carb - Honda HS520

If you're referring the port at the bottom of the fuel. That is a drain port and  not a fuel in port. There air in line on this carburetor.

Hmmm. I have never seen the drain line connected as you describe then. The drain and the air vent should be separate lines with no interconnect. Otherwords the six inch drain line should just be dangling free on one end and the same with the air vent line or at that the way I have always seen it done on other engines. It would defeat the purpose of either one as air vent line can not breathe and the fuel drain would not be able to drain. Either way there should be no fuel in the drain line except when you are draining the carburetor bowl. The air vent line should be feeding the carburetor's air bleed that controls the fuel mixture; when plugged it would cause an over rich mixture.
 
From here I would need to defer to those that have seen snowblower setups... If all else I would try replacing the Stay Assembly, Petcock part assembly. Depends on engine serial number as to which one you need.