A friend of my family recently sold her iPhone on ebay a few weeks ago, and started getting some interesting, and scary problems. My wife texted her, and the person who received the phone RESPONDED! Yeah, that’s really weird.
Our friend had gone into the phones settings and clicked the Reset All Settings option in the reset menu, but didn’t tap “Erase All Content and Settings”, and the phone was still getting the text messages (in this case, iMessages). Enter Wipe my phone, a free utility from Apple that’s included in the Find My iPhone app. We used that to remotely wipe the phone and we are no longer seeing anything weird with text messages or anything else.
Just a heads up when you’re selling your old electronic devices that may have some personal data on them. If I can help in any way, please let me know.