The stars you are referring to are called rogue or exile stars.
One way such stars are created is when one member of binary star system
goes supernova and loses a great portion of its mass. This reduces its gravitational grip on the other star causing it to wander off into what eventually might be intergalactic space.
Another way for this to happen is for binaries to come too close to a black hole where one is swallowed or torn apart causing a disruption of their gravitational relationship.
The black hole at our galaxy's center, for example, is said to have produced two rogue, or exile stars in this way.
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