We use the air valve lever on the fuel tank cap to cause the EU2000 to run out of fuel. This same valve should be turned off when transporting, or fuel could ooze out if the EU2000 is tipped over.
We've always either shut of the fuel on our old 2400W Honda model or used the air valve lever on the EU2000. No problems with either. The 2400 will re-start by third pull after a year of sitting (used during power outages at our cabin).
Hondas are particularly fussy about fuel sitting in the carb, which gunks the jets. When I worked at a Honda dealership, many Honda power products came in for repair due to this. I advised purchasers to let the carb run dry, same advice the small engine mechanic always gave.
