I personally prefer to make the error state part of the objects: Streams can be in an error state, floats can be NaN and integers should be low(int) if they are invalid (low(int) is a pointless value anyway as it has no positive equivalent).
It's fine to pick sentinel values for errors in context, but describing 0x80000000 as "pointless" in general with such a weak justification doesn't inspire confidence.I would agree, whether error values are in or out of band is pretty context dependent such as whether you answered a homework question wrong, or your dog ate it. One is not a condition that can be graded.
I view both of these as not great. If you strictly want to rely on wraparound behavior, ideally you specify exactly how you're planning to wrap around in the code.