Is it possible to have a star drifting through intergalactic space?
Yes, although they would be impossible for us to see, or at least impossible for us to identify as being intergalactic.
Stars don't form outside of galaxies or globular clusters, however when galaxies interact (i.e. smash into each other) material gets stripped off and some of the stars will become unbound to the new galaxy made by the merger of the two, where by unbound it means they have sufficient velocity to exceed the escape velocity of the new galaxy. These stars will then be exiled to the relatively empty space between galaxies.
'Rogue' stars also originate within the milky way. The supermassive black hole at the center of the MW is believed to occasionally sling one member of an inspiraling binary system outward at high velocity. These are deemed to be very rare events and unlikely to pose a threat to earth. About 5 such examples have been confirmed to date. See:
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