Yes, there are such regions of the universe. They are beyond the cosmic event horizon, which is the boundary inside which light, if it is emitted today, may still reach us sometime in the future. If it is emitted outside this horizon, the expansion of the universe ensures that the light will never reach us.

The cosmic event horizon differs from the particle horizon, in that the particle horizon represents the largest comoving distance from which light could have reached the observer by a specific time, while the cosmic event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future. The cosmic event horizon is also the limit where the relative radial velocity of distant Hubble-flow galaxies reaches the speed of light.
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