What are "change the quantity" textboxes at the Fulfill order page for?

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At the fulfilling order page there're "change the quantity" textboxes for each product or variant.
In what circumstances one would want to fulfill a less amount of a product than it was ordered by a client?

And would happen to the total price then? Namely, a customer has paid for 5 t-shirts, and one filfilled only 3 ones.