This was featured on "TJ Hooker", episode 43 but conceivably could happen in real life.
The cop (Hooker) is escorting a victim, who is a diabetic. While walking, she dropped the insulin that she needs to survive. The villain picks up the insulin and sets it afire, which is tantamount to to murdering the victim, because if she loses this batch, there may or may not be time to get more. If the villain keeps the cop and victim trapped in a "stand-off," the victim will definitely die.
The cop has a clear shot at the villain. If he shoots the villain, he might retrieve the insulin and save the victim's life. If he lets the villain conduct a "siege" and tries to rescue the insulin without disabling the villain, the latter will shoot him down in cold blood.
Is this a situation where a cop is allowed to use deadly force to prevent a murder (or two)?