Contractions can be used in any position in a sentence; however, homophone contractions such as "it's" and "they're" sound better when followed by another word or phrase. The reason is that the sounds of "its" and "it's" and "they're" and "their" are so similar that they can be confusing unless they are used with the context of an additional word.
I think it's less to do with homophone confusion and more to do with usage patterns relating the contracted part to a phrase rather than a single word [1] [2]. By the logic of the homophone explanation, the following exchange should be much more acceptable than a sentence ending with "it's" or "they're", but to me it seems equally strange:
