Hi there, I need to know if someone doing an HSS or transporter move & attack who happens to KO someone can end their move occupying the area of the person they KO'ed?

I seem to remember vaguely a situation with walls where if you attacked a wall at that speed, the wall would only become rubble when your movement was ended... or was that changed?

Yes they can because the remainder of the move happens after the attack resolves, and the attack resolves when the target fig is clicked for damage. If it is KOed it is removed from the board immediatly, so it would no longer be occupying that square, so it would be legal for you to finish your move by moving into it.

Well with unstopable you can move, smash a wall and move through the gap created. If it didn't become rubble as soon as you hit it then you couldn't move through the gap. I don't see why HSS should be any different.