Unilateral kidney failure is possible in cases of unilateral nephrolithiasis (kidney stones) however this would be painful enough to prompt someone to go to the ED where the imaging and labs others have mentioned will be done.

In the case of unilateral nephrolithiasis you would expect to see a patient with unilateral flank pain, CVA tenderness, and the urine studies would show red blood cells in the urine. This isn’t technically kidney failure per se, but is one of the ways someone without access to care may develop it.