There are many diseases that can live in us indefinitely. Do you recall having chickenpox when you were young? The virus that caused that disease still exists within you but luckily it is in a dormant state so doesn’t make you ill. However, under stressful conditions the virus can reactivate and cause shingles which is a painful disease.
There are other diseases that dont go away but you can still live with. Those that come to mind are some STDs like herpes. Left untreated you can have herpes for your whole life.
Chicken pox came into my mind too! More generally, any latent disease can stay in you for your whole life – these are diseases which are in the body, and not causing disease at the moment, but can reappear in later life. With chicken pox, this later reappearance is known as shingles, as Peter said. Another well-known disease that can be latent is tuberculosis (TB). It is thought that most cases of TB in the UK are from infections that happened many years previously, perhaps whilst travelling to places where it is far more common.