On the last note of Mozart's "Kyrie eleison" in his requiem, he chooses a stark and intense open fifth instead of a triad. What happens when a composer finishes...not correctly? Is this allowed?

When using old melodies which start and end on scale degree 3 (relative to major), Bach adapts this old Phrygian mode to his idiom, but this does create an unexpected ending. Even more surprising is the wild hellish chromaticism of the final passage leading up to the Phrygian ending of this "Kyrie" setting. Even by Bach's own standard, this chromatic passage goes beyond. 

Leo van Doeselaar plays BWV 671 (the focus of this episode and the text on the Holy Ghost) for the Netherlands Bach Society

BWV 669 (text on God the Father)

BWV 670 (text on Christ the Son)

Mozart Requiem II. Kyrie (excerpt): Public Domain recording