It happened to me too

I knew my alternator stopped working, however, I was hoping I could get to my destination before battery died so I kept going. Since I was somewhat prepared, I drove on the rightmost lane and I was able to pull over to the shoulder when the car finally died.

I agree that it is very dangerous driving with dead alternator. There will be no emergency flasher to warn other drivers if you can't get off the road before the engine shuts down.