It's probably what's left of the old gas filter .I think on the Mini's which is what a 110 is,I think they had a metal type filter with a piece of felt like stuff around it .Which could have hardened up .You could have sucked some crud off the bottom of the tank and plugged the carb .The kits BTW for that certain model of Zama,if that's what it is are very hard to find .
Another thing.Because of the age,which it's not a new spring chicken the fuel line could have a crack in it up above the level of the gas in the tank .You might get enough sucked into the carb to start it but it dies after a few seconds .
Minis which BTW are the most frustrating saw to work on ever made are famous for one thing .They either run great or they don't run at all .Fact I was given one,non runner that had the original McCulloch chain on it that had never been filed.