If you say to someone "I hope you won't stop checking in on her" And this person answers "Of course I will"
Does it mean "Of course I won't stop" ?
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Another interpretation is that the response is simply an elided statement.
In short, it might not, literally, mean the following:
Instead, it could, literally, mean the opposite:
But regardless of what the response literally means, I can't imagine it would actually be taken to mean that the person was saying they would stop checking in on her.
It's similar to double negatives:
That literally means a positive:
But everybody understands it to mean an emphasized negative rather than a positive.
While using a double negative in this way might be considered poor grammar and a mistake in formal situations, it's still entirely understood, and it would not be considered a mistake by the people involved in its informal use.