As objects cross the event horizon of a black hole, the light emitted by them as observed on earth, is frozen at the horizon. We never see the objects actually cross the horizon. But the frequency of the light continues to decrease. So using the red shift correlation with distance, we would observe these objects as being further and further from the earth.

However, this is not yet true for the horizon of the universe as the universe is not yet old enough for light from stars that are receding from us at the speed of light to have reached us. According to Loeb, that will require another 6 billion years of aging. There is such stars and such light heading this way, but it will not arrive for 5-6 billion years. The CMBR will disappear first in about 5 billion years.