Maybe this is old hat to you, but it's new to me. And exciting.
I was reading about the Nazarite vow in Numbers 6 the other night. I figured Jesus had to heal the sick, raise the dead, and forgive sinners. Since he fulfilled all the Law, including laws concerning cleanliness, separation, and corpses, he would have become unclean had he touched anyone with leprosy or a discharge or even been standing next to someone who suddenly died and fell on him. But we know he was sinless and perfect in every way when he went to the cross.
Touching a corpse, under the Law, would have defiled Jesus. Notice when Jesus raised Lazarus, that he didn't run into the tomb and lay hands on his friend's body. He simply spoke. We don't know from scripture, but I imagine Jesus embraced his friend after the graveclothes had been removed. He could never have done that with a corpse. When someone is raised from the dead, he's no longer a corpse! And therefore no longer something to be avoided.
A woman with a twelve-year flow of blood, required under the Law to be separated from the congregation of Israel, would have defiled Jesus by touching his garment; however, Jesus didn't do any of the prescribed rituals for cleansing after interacting with her. Instead, Jesus noticed that virtue flowed out of him when she touched him. We so often think of virtue as being moral goodness, but in this reference, in the original Greek, it's power. But perhaps it was both. The virtue (power) of virtue (holiness) demands preemptive cleansing. This makes me think she was healed just before (perhaps even a nanosecond) touching his robe!
Sickness, disease, sin, poverty, and death have no choice but to be reversed in the presence of such awesome holiness! Woohoo!