Can the molecule POOF exist?
There exists related anions called monofluorophosphate ion ($\ce{PO3F^2-}$) and difluorophosphate ion, ($\ce{PO2F2-}$). The hypothetical neutral compound, $\ce{PO2F}$ is called phosphenic fluoride. It is also observed that irradiating potassium difluorophosphate with gamma rays create free radicals $\ce{PO2F^{.−}, PO3F^{.−} and PO2F2^.}$.
Moreover, there also exist a polymer $\ce{(PO2F)_n}$ which is a decomposition product of a white solid of composition $\ce{P7O10F15}$. It was apparently named polymeric phosphorus oxyfluoride species. Its structure has been proposed by Wannagat and Rademachers1:

It is suggested that the parent ions of Group I result from the simple
ionization of a linear polymer with the general formula, $\ce{(PO2F)_n}$,
where each of the terminal phosphorus atoms of the chain is bonded to
two oxygen atoms, one of which is a bridging atom, and to two fluorine
atoms.


Conclusion: There is no such compound called POOF, but there certainly is a radical ion and a polymer of exact formula.
Notes and References

High molecular weight phosphorus oxyfluorides by D.W.Muenow, O.M.Uy, J.L.Margrave, Journal of Inorganic and Nuclear Chemistry, Volume 31, Issue 11, November 1969, Pages 3411-3415, DOI: 10.1016/0022-1902(69)80324-6
Other decomposition products were $\ce{PF5, POF3}$ and $\ce{P2O3F4}$: Technique of Inorganic Chemistry, Hans Boegh Jonassen, Arnold Weissberger Volume 1
Interscience Publishers, 1963