What happened in the eastern half of the roman empire after the western half collapsed under the weight of the visigoth and germanic invasions?

The Eastern Roman Empire continued to exist (for around 1,000 years more) and even prosper after the fall of the Western Roman Empire. This was due to the political stability in the east, it was also more populated, it's army was stronger, it was much richer, there was peace inside it's borders, and it's capital Constantinople was so well defended that it was almost impeccable. Al of this contributed for this part of the empire to survive than and for almost 10 more centuries plus.