The carb may have a blocked low end passage, or the pumper diaphram may have broken down, or as stated, there might be an air leak.
I had an old 3.7 cu inch (60cc) Craftsman of '78 vintage act like that, & it was the pumper. Kits are about $7 or so.
I originally thought it was the main seals going bad on mine, because of the way it acted lean, especially at low end. My brother told me it was the pumper...which it was.
Try Jacks. You could easily rebuild, or just swap out carb:
http://www.jackssmallengines.com/Pr...-Parts-2-Cycle/Carburetors/506450401/622670/s
Most chain saw use Tillotson pumper carbs, but I don't know what Husky uses.
One more possibility (but doubtfull in your case) is a broken down fuel line pickup in the tank. I had that happen also, but the symptoms were different.
Joe