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So it says in the BRB that no model may move off the table except for fleeing/pursuing models.

So what happens when a unit with random movement, rolls so that its movement would take it off the board. does it just stop when it hits the board edge? Or does something else happen?

Is the model fleeing or pursuing? No? Then it stops when it can't legally move any further.

As there is nothing saying something bad happens at the point, you just finish any other random moves and go to the next phase.

Yup. Unless you have permission to go off the board, you cannot move off the board.