You're likely referring to the attempted reconquest of rome by Justinian and the subsequent so called plague of Justinian.

It is possible the Eastern empire would have reconquered most of the now defunct Western empire. It's also interesting to me that the rise of islam can also be tied to the weakening of the Eastern empire due to this plague and other issues. Islam was quickly able to overrun large and very wealthy parts of the Eastern empire. Perhaps a stronger Eastern empire could have resisted that and islam would be largely forgotten to history.