You should check out Tennessee v. Garner, 471 U.S. 1, decided on March 27, 1985. In particular, Justice O'Connor's dissenting opinion. The case involved a 15-year-old burglar, Garner, shot in Tennessee by the police responding to a call. Garner was discovered hiding by a fence, was called out to halt, began to climb over, and was shot in the back of the head by a responding officer. Justice O'Connor, along with the Chief Justice and Justice Rehnquist sided, more or less, with the police. The majority opinion, they said, "effectively creates a Fourth Amendment right allowing a burglary suspect to flee unimpeded from a police officer who has probably cause to arrest, who has ordered the suspect to halt, and who has no means of firing his weapon to prevent escape. I do not believe that the Fourth Amendment supports such a right..."
Obviously, there could have been cases decided since then that have made other differences...
Oops. Make that "and who has no means short of firing his weapon to prevent escape..."