That's very strange, indeed. What is the make and model of your device? Are you using a messaging app other than the one that came with your device? Have you tried restarting your device immediately after you delete the messages?
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I have the same thing happening to my phone (just did a google search to see if anyone else was having this and came to this thread). Samsung Galaxy Edge 6+. My husband's phone, same model, on this same account does NOT have the issue. This problem just started maybe within the past 2 weeks or so. I do run Facebook Messenger and all of the Google apps like Hangouts, but I have used these same apps concurrently for the past year without any issues. I'll get say 10 different message threads in over the course of an hour or two (some from other Verizon #s, some from other carriers, some from text -based services). The ones from friends will have lots of back and forth messages within the thread, while say a store text message will just be a coupon . I'll delete the 10 threads and all the messages within each thread. Completely blank message box. Maybe 30 minutes later all of the deleted threads and message will suddenly reappear - and they ALL show up as unread messages. Major deja vu! But this problem is random - I can't find a pattern. The only difference between mine and my husband's settings is that I've disabled automatic backup - I don't want anything backed up via Verizon's cloud. But it's been like that for a year now. Maybe something changed, and it's creating an issue within the past say 2 weeks?
This would give me deja vu as well Donna! We want to ensure your deleted messages stay deleted. Do the threads return to all your messaging apps or is it just happening with one of the apps you use? Do you use another backup service like Google Plus on your phone?
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If my response answered your question please click the _Correct Answer_ button under my response. This ensures others can benefit from our conversation. Thanks in advance for your help with this!!