You could compare the system to a siphon. In a siphon, liquid will flow upwards through a pipe, provided that the pipe is completely filled with liquid and, having reached its highest point, goes down lower on the other side of its highest point! This may help to make the behaviour of electrons in your set-up seem less strange. A proper explanation, though, needs the concept of potential, closely related to voltage. Here is the explanation...
Negative charge, if it is free to move (that is if a conducting path is provided), will move up a potential gradient, that is from a region of lower potential to one of higher potential. The closer a point is to a negative body, the lower the potential of the point. So in your set-up the negative body will put the sphere at a negative potential. [Being a conductor with no movement of charge the sphere will be at the same potential throughout.] So negative charge will spontaneously flow to the ground from the sphere if a conducting path is provided.
Added later...
But can't we understand what is happening in terms of forces? Surely electrons are repelled to the surface of the far side of the conducting sphere by the negative charge and won't spontaneously go back to the 'near' side of the sphere, where the 'escape wire' is to be connected? Here's what we're missing... Because electrons have been repelled to the far side of the sphere, leaving the near side surface depleted, that is with a positive charge, there is another electric field: one that is set up by these induced surface charges. This field is in the opposite direction to the field from the external charge; indeed it's what stops the displacement of electrons going on and on. Equilibrium is very soon reached when the field due to the induced (displaced) charges is equal and opposite to that from the external charge, leaving no resultant field in the sphere! Or, in terms of potential, all parts of the sphere are at the same potential. So that's why, when the escape wire is connected, electrons from the far side can travel to the near side.
