To allow the driver to fully hand off control to the car, the car should be able to handle it all. The driver assist functions we have available on certain cars nowadays are a great start in working towards full control by the car: now the car will intervene in certain emergency situations, when that's all settled, we can think about giving off control of the rest of the ride as well. For fully automatic drive, the car should not rely on human intervention, ever.
I think it is perfectly reasonable for a self-driving car to (safely) pull over to the side of the road and come to a stop when there is a scenario which it is unable to handle on it's own.
Situations such as out of gas, major engine problems, tires no longer functioning properly, road closures with no available/allowed alternate route, or other 'I do not know what to do next, so I came to a stop in a reasonably safe location to ask for help' scenarios.
Admittedly you will want some way to verify that the shoulder is present when you do this, but other than that, stopping by the side of the road should be a valid failure mode.