I can only think of:
1. When coliding with another massive object, or:
2. When rotation is so fast that the star is torn apart by centrifugal forces. (unlikely in both cases)
Although both cases are highly improbable, the latter figures prominently in an alternative model I've been toying with to explain the anomalous distribution of angular momentum with in our solar system.
I believe the more akin an object is to its corresponding black hole (radial density, charge and angular momentum), the less chance it has of spontaneously bifurcating.