From your description it looks like he is suffering from hepatorenal syndrome(HRS), which a kidney
failure secondary to severe liver disease. (Although there can be other causes for renal failure
such as infection)
If it is HRS, then the kidneys are unlikely to recover till the liver improves or if a liver transplant
Most likely he is receiving terlipressin injections, if he fails to respond to it, dialysis
will be needed as supportive care. He may improve his kidney function if it is due to some other cause rather than the liver.