This one contains comma splices and some awkward wording. Note the period, not comma, after family in the corrected version.
At least the (inappropriate) ellipse at the end has the correct number of dots. 🙂 There shouldn’t be a space between the last word and the ellipsis, though.
A stranger arrives on your doorstep and claims to be related to your family. Not only that, but they have an unbelievable story to share with you.
If you really want to streamline the first sentence, try this: A stranger arrives on your doorstep, claiming to be a relative. (Streamlining/shortening sentences is not always a desirable thing, by the way. Using only very short sentences and small words, no matter how good those words are… Well, you can probably guess how that sounds sometimes.)