We would most commonly say "The most amazing things have always happened after a person has given up hope" Your second item feels slightly more awkward due to the juxtaposition of tenses, however it doesn't seem wrong in the sense that when using unusual combinations of tenses they to a certain extent turn into hints for the listener to construct a feeling and a scene, and it's the feeling of your constructed scene you feel more than whether the tense combination is right or wrong. I suspect people do use your second form though probably not in informal speech. d
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Anonymous"The most amazing things have always happened after a person gave up hope"I read the prepositional phrase, "after a person gave up hope", as a point in the past, a time marker.