I have this same issue. The instructions give the same result as previous responder's instructions. After draft message text is deleted, tapping the back arrow brings me back to the conversations screen, and "message saved as draft" pops up, with the text that I had just deleted showing in the message balloon.
You've come to the right place for help. Let's find out more details here. What messaging app are you using (standard app, Verizon Messages, etc)? When did this start happening?
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