Can a point in empty space be motionless with respect to light? Being that the speed of light is constant throughout the universe, can a point in empty space be motionless with respect to light? 
 A: In a non-accelerated reference frame, a point or a particle cannot be motionless wrt. light, for the reason that busukxuan mentions: All observers will measure the speed of light to the same value, c.
But in an accelerated frame, such as an expanding universe, it is possible. For instance, galaxies that are farther away than about 14 billion lightyears, recede from us faster than c. The light that these galaxies emit in our direction, leave the galaxies at speed, and always has a local velocity of c. But since the galaxies move away from us faster than c, the light initially also moves away from us. As the light travels through space and approaches us, it will eventually pass the point where the expansion velocity of space is exactly c, as measured from our position, meaning that at an infinitesimally small period of time, it will be motionless wrt. us. Immediately after, though, it will start moving faster and faster toward us, until much later it reaches us, at which point its speed will reach c.
A: Your whole question relies on the fact that you can define a rest-frame for light.
Assuming that the constant c appearing in special relativity is indeed the speed of light, there is no such thing as a rest frame for light.
More specifically it is trivial to check that Lorentz factor tends to $\infty$ as you get closer and closer to light speed, hence the impossibility to boost into a photon rest frame.
