Based on DVK's response to a comment, I think it's possible to have a work be Hard and Soft Scifi; it's just usually not at the same point in the same work.
Warning; long rambling post follows
Short form: Lots of SciFi does this, when the sections of a story are really almost independent. Strange in a Strange Land is as an example, as is Number of the Beast
All that said, this is really dependent on your definition of Hard vs Soft SciFi.
An example would be Heinlein's 'Stranger in a Strange Land'; like most Heinlein works, it has a very solid grounding in understood physics and science. His analysis of the needs of a convalescing space traveler even resulted in him describing one so well, an inventor was declined a patent for the Waterbed, on the basis that Heinlein's description constituted prior art.
Even Valentine Michael Smith's almost magical abilities are explained as related to psychic abilities he learned on Mars; not magical, but simply exploiting details of physics that Humans don't yet understand. (As an example, instead of simply making something 'vanish', he gives it a multi-dimensional 'push' and tips it 90 degrees out of this reality.)
But that's the beginning. Then things change.
Much of the rest of the novel is an attempt to parody / satirize / critique / change various social norms. Although Michael still uses (primarily) the same abilities, the explanation is slowly transitioned to it having more to do with the nature of reality than anything else. The eventual ending shows us an early view of Heinlein's 'World as a Myth' concept, with our hero
transitioning into a role as an 'Angel' or equivalent, giving confirmation to his assertions that existence is really a form of consensus reality, with everyone being part of the creative team. ('Thou art God' is the phrase he confuses people with, while trying to explain this in the books.)
Although he doesn't eliminate or change the science from the previous parts of the book, the Philosophical realization of the nature of reality kind of 'hand-waves' any subsequent actions; to me, that moves the story into the realm of Soft SciFi -- explanations (or reasons) are no longer needed since our understanding of the nature of reality has been shifted. (As Maureen would point out, many books later, Reality is not logical; it's whimsical.)
Don't get me wrong; I love the book.. but it's really two books -- the origin story, with some hard (if theoretical, at points) SciFi, and the story of his Ministry, with Soft SciFi allowing us to suspend disbelief at what he does, and using him as an Human with the Perceptions of an Alien to hold a mirror up to society.
An arguably better example would be 'Number of the Beast'; it starts out with a Professor inventing a device that seems to allow travel between universes, but is VERY concerned with everything from the engineering of the space ship, the programming of the computer, the physics of space travel (and simple ideas like checking the air safely on a new planet), even scientific and practical details about building an 'off-the-grid' hideaway -- all stuff you would expect from an intelligent, well-versed-in-science crew. And, then, by the end of the novel, having
realizing that the universe is based on belief, not science
almost anything can (and does) happen, and is hand-waved away by the aforementioned understanding. See the details of the party at the end of the book for more details; but there fantastical elements that are simply never explained, as we are to understand (by this point) that explanations are
unnecessary, as belief is what causes reality.
Again.. Shifting for hard-headed logic and science, in the beginning, to an almost Fantasy world, by the end. Hard->Soft, as the story goes along.