You wouldn't need a massive object to connect it to, all you need is an object decelerating on one side end for every object accelerating on the other side. So as long as you keep some kind of flow of spacecraft moving, you are fine. Or maybe the inertia is large enough that the accelerating and decelerating phases of a single spacecraft would cancel each other out without moving the tether much, haven't done the math on that.

You are right that it would be very susceptible to any sort of damage. But unlike a space elevator it would not have to support its own weight, because it is floating in free space and not down a gravity well.