Box is very amenable to being any shape you want. You can clip it back into shape over time. Your pyramidal shrub would have needed continued shaping even if the top hadn't been damaged.

think in tree shrub time... which is years ... or even decades ... not one season or two ...

all plants releader ... if you have the patience to wait for it ... this injury is not going to change the genetics which tend toward pyramidal

yes.. you can guide it along ...

but i would give it at least a year and a half to see how it sorts itself off ... thru next summer ..

with no insult to the roots ... it should respond quick enough ...

perhaps next fall .. you can select one leader.. and remove any extras ... to further the process ..

now.. all that said ... if its right out the front door.. and simply going to drive you insane ... just get rid of it ... and move on with your life ... its not some rare specimen ... replace it.. if it will cut out any stress ...

maybe move it out back.. where it wont bug you so much.. and plant something else here ...

ken

The piece in your hand could make about 100 cuttings if you want free new plants.

I've been thinking of moving them anyways, this might be a good time. This is the north side of the house, and there is a small porch awning above...so these only get sun till about 9:30 in the morning. The back side of both is starting to get bare where the sun never touches them. Difficult spot for a small evergreen anyways.

Shrubs don't have "leaders" :-) That is a characteristic specific to trees and even a great many trees do not produce leaders. As floral noted, the missing/damaged parts will regrow or the plant will fill in. And to maintain a proper pyramidal form, it will require pruning anyway.

pyramidal plants ... must have branches/leaders with atypical dominance.. else they wouldnt have the suggested form ...

https://duckduckgo.com/?q=atypical+dominance&t=ffcm&ia=about

and when one is broken.. or pruned ... another will take over said dominance ...

it will not turn into a spreader of green blob form ... genetics does not change.. due to injury ...

great to hear ... that you might be better off moving them.. outta sight.. outta mind.. and you can quit cursing the roofer ... lol ...

ken

Apical (not atypical) dominance is one thing.....a "leader" is something else altogether. All upright growing plants have apical dominance but very few actually develop a leader.

That box is only pyramidal because it's been pruned like that. It is not naturally that shape. It could just as easily be made spherical, spiral or even a cube. The OPs plant would most certainly turn into a 'spreader of green blob form' if it were not routinely shaped by pruning.