Although Munich managed it with Javi Martinez (rather more easily than the rags with Herrera) but that is, essentially, how a buy out clause works. Club A gives the player the cash and the player gives the cash to club B.
Technically of course, Sanchez could actually terminate his contract with Arsenal, join another club and then they'd both be liable to pay Arsenal an unknown amount, as decided by the Court of Arbitration for Sport. This would be based on his 'market value' which would probably take 3 years to decide. Given the likely chaos that would follow any such move, I suspect there might be some PL agreement not to sign players who do this, although that is pure supposition on my part.