This is normally safe. It will save you from having a bigger procedure. There are a few risks or complications, as with any medical treatment.
If you are having a liver biopsy, then there is a risk of bleeding from the liver. However, this is generally very slight. If the bleeding were to continue, it is possible that you might need a blood transfusion. Very rarely, an operation or another radiological procedure is needed to stop the bleeding.
If you are having a lung biopsy, it is possible that air can get into the space around the lung. This usually does not cause any real problem. However, if it causes the lung to collapse, the air will need to be drained. This will be done either with a needle or a small tube, put in through the skin & you will remain in hospital until this is removed.
Unfortunately, not all biopsies are successful. This may be because there may not be enough abnormal tissue for the pathologist to make a definite diagnosis. If this is the case they you may be recalled for a repeat of this biopsy procedure or else your doctor may decide to tray and gain the tissues sample using a different method. You will be told about this by your doctor.