Assuming that there is sufficient evidence of the identity of the at fault party. There does not need to be an actual impact between vehicle and pedestrian.
A person could also be injured taking evasive action then they could pursue a claim and could pursue a claim against the at fault driver. These cases are handled like most other injury claims. So for instance you were involved in a slip and fall in a supermarket and you knew that there were witnesses but you never gathered their names and now you can’t find them. In that case you are going to be largely out of luck, if nobody observes the hit and run and takes down the information of the driver that caused the situation. If you don’t get the drivers license plate or you don’t recognize the driver and they speed away, a description of the vehicle perhaps may be a bit helpful but obviously you need to do what you can do to get the information right away before an unscrupulous driver has the chance to drive off. If you can’t ascertain who the driver is then, very likely you’ll be unable to pursue a claim. You might still be able to pursue medical treatment through your own personal injury protection insurance. But because the accident involved a vehicle even though you weren’t in one, because that vehicle hits and runs, speeds away without information you will be hard pressed to come up with any ability to make a claim for bodily injury.