The most serious consequence of acute pancreatitis resulting from biliary obstruction is

The most serious consequence of acute pancreatitis resulting from biliary obstruction is the development of circulatory shock.

In rare cases, acute pancreatitis can lead to necrosis of pancreas tissues. Pancreatic enzymes may get into the bloodstream and cause inflammation and damage to other organs which then can lead to shock, respiratory failure, kidney failure and other complications. This is a very serious situation which can be fatal.