At the surface of a black hole, at the Schwarzschild radius, time is infinitely dilated (time does not flow at all)! No matter what the color may be, the light coming out of the star must get redshifted to infinite wavelength, all the way out of existence!!
Bellow is a figure showing how much light gets redshifted at various distances from the black hole and at the Schwarzschild radius.
The closest that light can get to a black hole and not fall in is at 3 Schwarzschild radii, also called the radius of the innermost stable orbit. Any light or matter that gets closer than 3 rsch will fall into the black hole. Thinking back to AGN or accreting black holes, this innermost stable orbit is the inner edge of the accretion disk where gas from the accretion disk finally falls into the black hole.