There is also the discussion of a karmelit – a “in between” space, neither public nor private. It is forbidden to transfer from karmelit to pubic or to private. A hand reaching out is like this in-between space – it does not present a problem until it returns to the body with the object. One can imagine a person standing with hand outstreached between two domains all Shabbat long, unable to move until Shabbat ends!
The truth is no one would be required to do this, but guilt or innocence would depend on whether the initial movement was intentional or not!