"Did" is only used in the affirmative for emphasis:
A. He wasn't injured during the shootout. B. You are wrong. He did get shot.
That said, the phrase "the person to have got shot" is equivalent to "the person who got shot." The perfect infinitive "to have got shot," which is passive (similar to "to have been shot"), refers to the past, and means "who got shot" (or "who was shot).
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