What should we do when the selection step selects a terminal state?

In Monte Carlo tree search, what should we do when the selection step selects a terminal state (i.e. a won or lost state), which is, by definition, a leaf node? Expansion and simulation is not in order, as it's game over, but does the tree (score/visits) need to be updated (backpropagation)? Won't this particular node be selected continuously?

But you can improve that: If the leaf is losing, you can give it a very large negative score or even $$-\infty$$, so in the next selection step it surely won't be chosen, unless other moves are as bad. But if it is a winning leaf, you not only can give it a very big positive score or $$\infty$$, but also add a negative score for the immediate parent, so the parent won't be chosen, as it is obviously a losing state for him. This way we can save some simulations. I had encountered that situation many times in my game and Monte Carlo tree searches.
Suppose the parent has $$200$$ unexplored children, $$10$$ of which are immediate wins for the opponent. Your search may explore $$100$$ non-winning children and have a score of 80/100. But then it encounters the terminate child. After that, normally, it would have $$80/101$$, so, still, a big chance to be chosen in the next iteration. And it would take many iterations to see that this is not a good move, as it would need to get like $$80/150$$ or more. But if we cancel out the score or give it a negative one like $$-1/101$$, then we ensure it won't be chosen.