Unless it is quite early in the game, the place of the Byzantine Emperor (with at least 1 heir in his stack) is not on the batlefield. My Emperors are actually administrators, stewards and sometimes a bit crack brained or lazy but are not really keen on leading the Imperial armies from the front. If I have spare heirs, I send them as generals. (you can see the idea to prevent a sudden ending of the dynasty here).
Usually my Emperors are very harsh towards their generals. It's most unforgivable to run from the batlefield, and the good runner/doubtful courage reputation destroyed the career of not one or two six star generals. If the general was truly great (which usually mean he defeated one or two armies of the mongols in High) the he might become governor of one of the Mediterranean islands and even command their conquests. If they are captured, this usually means ability to take the responsibilities of their mistakes and are ransomed back with the rest of the army. If they die ("Your general has fallen before the enemy onslaught"), their family receives honours for the loyal service of their member. If the general retreats in good order (withdraw buttons) he almost always receives a second chance. As for the people, if the defeat is truly humiliating, I sometimes deny ransom. But usually, I think they have done their best and deserve to be ransomed back. Then I retrain them to a full size units, which usually takes years with all the units. If I ransom back some mercenaries, nothing can be done and they are almost immediately sent back to the battlefield unless the units is too small (and ransomed back because of other units)
If you ever play with the Byzantines in High starting campaign with limited Varangians guard (say no more than 1-2 units per stack) or in Late, you will clash with a low morale and outdated army. Every battle against a Catholic opponent is a challenge. The key to crush a Catholic is to have more resources and more provinces to rebuild your army, even if you face a defeat. Victories are also often expensive, so more provinces are not a bad thing.
Bookmarks