Let's go over the teams:
Anaheim - Doesn't need an RHD
Arizona - They need forwards themselves.
Boston - Charlie Coyle? But they don't need Faulk really.
Calgary - They don't need Faulk.
Colorado - They have all their positional needs filled.
Columbus - Ditto + they can't give up any more forwards.
Dallas - Best forwards are too old and expensive. Already good on defense.
Detroit - Andreas Anthansiou, Anthony Mantha, Gustav Nyquist. Detroit needs good defencemen. They're in a rebuilding year and they got better forwards coming up the pipeline. There could be a trade here to be had with any one of these three guys as part of the package.
Edmonton - They have nobody you want.
Florida - It would take Faulk+ to get one of their cost controlled forwards; they have a really good top 9. Mike Hoffman I could see but he needs a new contract by the end of the year.
LA - Neither team has what the other wants.
Minnesota - They good.
Montreal - They have RHD, they need LHD. Would work though, they have a bunch of depth forwards.
Nashville - They definitely do not need Faulk.
Devils, Rangers, Islanders, Flyers - They covered.
Ottawa - Faulk is too old for their team.
Pittsburgh - Nick Bjustad maybe? Something like that.
Sharks and Blue - They good I think.
Tampa Bay - lol
Toronto - lol
Vancouver - Jake Virtanen.
Washington - Nah.