I know, pics or it didn't happen so I'll get that out of the way.
As you can see I have a 266 xp that was acquired by my dad, a career logger. He got this saw (free I think) and planned to use it for a firewood saw, the PO purchased it new and said it would run great a day then not run for the next few so he tossed in a corner where it sat until lately. The condition lends credence to the story. Well, now many years later dad got it and said the same thing. Dad changed the carb, fuel line, filter, plug.... and maybe some other small things and it still does the same.
I ran it yesterday half a tank and it ran fine. Idles fine runs at any angle. Starts when hot. They say when it acts up that it acts like a carb issue. Wont idle wont tach up. Hard to start, but it will start. The problem can start warm or cold, not necessarily any pattern to it. I will run the saw and try to get a better idea of what the issue may be, but is there anything to check based on symptoms or maybe on this particular model or generation of saw, which is far older than I'm familiar with.
Also I'll disclose that while I'm a 20 year industrial machinery specialist, and a car restorer and atv mechanic in my spare time, my 2 cycle knowledge is limited at best. I have a tecate 250 and had a banshee and I've fixed a dirt bike or two but that's about it.