When people use the word jaywalking they are usually referring to crossing between two intersections, which is sometimes called a mid-block crossing. People do this all the time safely and don't get hit. But then the question becomes what if they do get hit, could they still have a claim against the driver who hit them?
When a car hits a pedestrian who is trying to do one of these mid-block crossings, there is a possibility the driver could be held responsible. It ultimately comes down to was there fault on behalf of the pedestrian or was there fault on behalf of the driver. A pedestrian can't simply step into the path of an oncoming car which would put them at fault. However, a car can't be speeding, distracted by using their cell phone or something else that would cause them to not slow down or avoid the pedestrian. So the short answer is a pedestrian can have a claim even though they were making one of these jaywalking or mid-block crossings.