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if you tank shock an enemy that is between solid cover and table edges, and it fails its eladership. does that cause a fallback off the table edge?

If you catch an enemy model with your vehicle so that it can't get out of the way due to impassible terrain such as table edges, it automatically destroyed.

By solid cover I assume you mean impassible terrain? They are placed in the nearest place they can move out from under the tank.

If you have an L shape of impassible terrain with the board making up the 3rd edge making a U then the models will jump out behind the tank where it drove in (until there is no room to fit out that way without passing through other models in their unit) at which point they will get squished.

Basically there are in reality practically no situations where tankshocking results in squished guys.

@wtnind, that applies to units that pass their test but end up under the tank's final position. The OP mentioned the unit failed it's test so it will fall back before the tank's movement has finished.

Normally, a Falling Back unit does so directly towards their own board edge (in missions where they have an 'own' edge) by the shortest route possible.

Difficult terrain makes no difference, but the enemy cannot fall back through Impassible terrain.

If their shortest path is blocked by Impassible terrain or other models they are allowed to move around the obstructions for the shortest path to their edge even if this means moving away from their edge. So if there is a gap, they can escape. If you have completely blocked them in such that there is no way past your vehicle (remaining at least 1" away) and Impassible terrain, they are simply destroyed rather than forced off the edge (no difference though really).

Reference: BRB page 30.