Here's a link to a story that shows the basis of the self-defense claim. He said he thought he saw a weapon in the thief's hand, and thought he was about to be shot.
http://www.thehighroad.org/archive/index.php/t-474161.html#.UVK4XfP4dpY.gmail
Here’s Washington State Law; note that it pertains to citizens, not law enforcement, who are covered in another point of the same chapter:
RCW 9A.16.020
Use of force When lawful.
The use, attempt, or offer to use force upon or toward the person of another is not unlawful in the following case(s):
(2) Whenever necessarily used by a person arresting one who has committed a felony and delivering him or her to a public officer competent to receive him or her into custody;
So in theory, any citizen can use whatever force is necessary to arrest (i.e. stop) a felon. However, the Tennessee v. Garner case must be taken into account for citizens as well as for LE; and the gist of that is that you need to assess and balance the risk of using force against this person vs. the risk of allowing them to escape. Are they going to harm someone? Have they already done so? How dangerous are they? That’s all Garner requires us to articulate.
There are certainly cases in which I would shoot a fleeing felon in the back, LE or not; and that decision would arise out of a conviction that they represent a totally unacceptable danger if allowed to escape. Both the Law and Garner envision and allow for this kind of possibility.
Texas does, but it has to be at night. TX Sec. 9.42. DEADLY FORCE TO PROTECT PROPERTY.
You certainly can in Texas.