come to an end, reach, arrive at, finally
訖 centers on reaching a final point: coming to an end, arriving at a destination, or finally completing something.
訖 combines 言 (speech, words) with 乞, which likely contributes the sound and may suggest the idea of reaching a limit or end. The exact historical development is uncertain.
Words (言) that beg (乞) for an ending: imagine a long speech finally reaching its last word, coming to an end.
For キツ, picture a kitsune (きつね, fox) arriving at the end of a long journey: kitsu -> キツ, and the fox finally reaches its destination.