This has been a thing on some of my exposed end rafter tails over the years at various houses.
There is one troublesome exposed tail on this current house. It may be peculiarity of the lower cost/spec/middle houses we poor folks end up in. Basically the builder/roofer and naked homeowner depend on the piece of shingle overhanging enough to keep the brunt of the rain water off the painted wood.
Anyway I have peeled the loose paint, allowing to dry now that our dry season is near. Will sand, then treat, primer and repaint in the summer.
I had some kind of chemical idear on helping. With both extending the drip and preventing growth by nailing a small pure zinc sheet metal square under that small shingle tab portion. We shall see!