Some trees can create adventitious buds in places where there were no buds or branches before. More often, trees have dormant buds near where they may have once had branches. In either case, exposure to light or a major loss of wood higher up in the tree may cause these buds to sprout and grow into new branches. However, this re-sprouting on old wood becomes less likely as the tree gets older and is less likely in evergreens than in deciduous trees. I have no specific knowledge of cedar trees in this regard, but my guess would be that cedars and arborvitae might be a bit more likely to re-sprout on old wood than a typical evergreen. Nonetheless, I would not expect much if this is an older tree.
This is not to say that this tree will never look decent. As jmusser notes in his/her answer, existing branches may, in time, be able to grow into the empty section. Thoughtful pruning as well as watering and fertilizing can help the tree accomplish that, and it may also help the tree the wall-off and grow around the serious wound it has.
You do need to remove the rope from the healthy side of the tree. If the tree has already enclosed the rope in bark, you may need the advice of an arborist on how to deal with the rope without further damaging the tree. Indeed, if this is a large tree, that is if it would require two people to remove the dead section, I would encourage you to get a arborist to evaluate its long-term health and safety. It is too bad the previous owner did not do that. If the tree had been properly bolted or braced, you might not have this problem.