How much of the old stem should you leave on the tuber?

My experience so far. I planted this plant for the first time last
year. The lady that gave them to me said just dig them up shake off
most of the dirt and put them in plastic shopping bags and hang in the
garage. I did and a good amount of my tubers turned to mush. I think I
put too many in each bag and I should have dried them out a day or two
out side in the sun to get rid of the extra moisture. I guess it is a
fine line. They are a live plant that can't dry out but you can't have
too much moisture either.