Something rather freaky happened a little over an hour ago. First, for those who don't know how StreetPass works, your Mii is shared on your 3DS and sent to others over StreetPass Mii Plaza. Both systems normally must be physically within a few feet of each other for this exchange to occur. However, I have done something that seems physically possible.
A week ago, I had a 3DS that I've had for several years with the Cat Mii. Last month, I picked up a used 2DS so I could have a secondary system and gave it its own Zoroark Mii. A couple days ago, my 3DS was starting to have issues with the buttons so I performed a system transfer, migrating all the content from the 3DS to the 2DS. All previous data (including the Zoroark Mii) was erased on the 2DS, and after the transfer the data was erased from the 3DS. Thus, I was left with a freshly formatted 3DS and a 2DS containing the data that was previously on my 3DS. I put a new Mii on the 3DS, carefully copying the features from the previous Mii (I had sent it to the Cat system for safekeeping) and giving it the same name of Zoroark.
However, I took a look at the StreetPass Mii Plaza earlier today and noticed a doppelgänger:
I somehow managed to find the ghost Mii?! Let's make sure...
Hm, the last played software was indeed the last thing that I used on the system (Mii Maker, to send the Mii itself over before erasing). Let's check the puzzle pieces.
Huh. Even those are the same. Let's see if it's on the other system...
34 tags? Well, that's definitely a confirmation that it picked up the signal of the previous data, as even a tiny difference would cause it to appear separately. (Notice the current Zoroark in the second row of Miis on the 2DS.)
Well, after thinking for a while, I think I figured it out. If you give up, check the spoiler.