The companion star orbiting in the direction of the black hole would pick up momentum and plunge toward the black hole. In accordance with Newton's third law of motion - action-reaction - the other binary companion would go whizzing off with the same velocity but opposite direction away from the black hole.
In just a few thousand years the star would ascend out of the galactic plane and hurtle deep into intergalactic space. The persistent tug of our Milky Way's dark matter halo would slow it down but the star would never fall back into the Galaxy.
So far at least 16 of these so-called hypervelocity stars are known. They were first hypothesized in 1988. But the first one wasn't detected until 2005. Hot and bright blue short-lived stellar runaways have been picked out because they are not native to the old stellar galactic halo population, they had to travel there. Also, the torturous Milky Way core - a stellar Monster Truck assembly plant - favors making massive stars in binary pairs.
However, it is not impossible that a sun-like star in a binary system could get the boot too. It would carry along any planetary system.