Any carburetor can gum up as the gas evaporates, and ever since oil injection, I don't think 2-strokes are any worse than 4-strokes. Running the engine 'til it dies doesn't get all the fuel out of the bowl, and may leave the main jet immersed even though the fuel level has dropped below the slow/idle jet. There are any number of fuel additives and sprays.
Mercury has Quickleen and Fuel System Cleaner, in addition to PowerTune decarboning spray.
Bombardier has 2+4 Fuel Conditioner, in addition to Engine Tuner spray.
Yahama has Ring-Free.
I forget who makes it, but NAPA carries Seafoam Motor Treatment additive as well as their Deep Creep decarbonizer.
And of course, there's Chevron's Techron, and I use the more expensive concentrated bottle.
Mercury was known to have problems with ethanol fuel, but my manual says it's okay to use fuel containing up to 10%, just don't use methanol. Not sure when that changed.