It's not necessarily the low testosterone that is causing the higher risk of death in most cases, it's their bad lifestyle/disease that increases the risk of death, the low testosterone is just is symptom of the bad lifestyle or disease. For example, type 2 diabetes increases the risk for death and type 2 diabetes causes low testosterone. Or being obese increases the risk of death, and also causes lower testosterone as a result. Low testosterone is just a marker for poor state of the body in a lot of cases. If the body is restored to a normal healthy state by changing lifestyle or addressing the disease, natural testosterone will rise back up to normal to reflect this healthy state.