As seen from far away, there will come a moment when the last photon emitted by the star has been emitted in the rest frame of the star's surface just outside the event horizon. When this last photon reaches you at an enormous redshift, the light from the star will have been extinguished. The surface of the star, as seen from your vantage point, may take an eternity to fall inside its horizon, but as seen from the surface of the star, it only takes a few seconds. Black holes, to the external observer, are an 'asymptotic' solution to general relativity, which may technically take an eternity to form in our rest frame, but they form nevertheless because the physics of the freely falling observer will see this event as a very well defined and fatal one.