My husband had a lung biopsy done and it resulted in hemothorax he was put on a ventilator for two days and remains hospitalized is the hospital responsible for bills of overstay ?

No, of course not: Pneumothorax and hemothorax are two of the known complications that can happen with a lung biopsy if a patient is unlucky. A patient is responsible for his bills if he has a good outcome, a medium outcome, or a bad outcome; as long as it isn't some truly strange case in which the doctor(s) and/or hospital did something unusually bad or criminal.

Keep positive: As noted, pneumothorax and hemothorax known potential complications of lung biopsy. Lung biopsy is often performed on "unhealthy" lung tissue. There is no way to guarantee a "perfect outcome". It sounds as if he is very sick. Our best wishes go to you.

Probably not: this is a known potential complication of having a lung biopsy