That is a long time for a birch stump, I am surprised it didn't rot by now, I have several apple and apricot stumps left from infected trees I cut down, they have lost their bark and started to break down where water was held, I kept putting manure all around a stump and watering it as it dried out but it do much so I am just waiting for them to do their own thing, I figure another 10-15 years before they are gone at this rate.