Deleted text messages are truly GONE. Nobody can access them. Unless you have a program installed that archives/backs up messages. In that case, deleting them from your phone won't delete them from the backup.
If you have multiple devices on your iCloud account, like an iPhone and an iPad or computer, iMessage might be receiving your messages on those other devices.
We appreciate you taking the time to reach out to our community member forums regarding your text messages. As 47seijar indicated, the messages are gone from your phone unless there is a backup running, or if another device is sharing a messaging capable UserID with you, such as an Apple ID. Do you share an Apple ID with anyone else? Do you use the Verizon Messages app?
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