This man could not help himself. He was totally controlled by demons, thousands of them. So violent and so strong was it that the other human beings could not control him either. He was in torment - totally controlled and he had no free will of His own. This is why Jesus confronted such situations. It is all of Jesus, not of human effort. He wanted people to see what He could do and who He was in situations where people had no control. He places us in circumstances that are totally beyond our authority and control, mainly to show us that He is in control.
Demons, by the way, cannot possess a believer because the Holy Spirit lives inside of a believer and possesses a believer. But Satan can harass us and hassle us from the outside in circumstances, mental pressure, emotional pressure, physical pressure, and circumstantial pressure. But from the inside we have Christ. All of this is to pressure the human side of life, not the spirit side of life.
The word "your" is a personal pronoun in the gentive case. Genitive case expresses possession. In English we translate it "your." But it is literally "the faith of you," meaning the faith that is belonging to you. He did not say that she produced it, that is a different pronoun. That is what is called a reciprocal pronoun: "the faith that you produce." That is not what He said and that is not what He used. He is telling her, "The faith that is persuading you; that persuaded you to come out and touch My garment that you would be healed, that is the faith that belongs to you." It was given by Jesus as a testimony to the crowd, around as well as to this woman, that she would be healed.
He will not allow us to find security in any other human being or in any other thing. He will not allow us to find happiness in anything else other than Him. And He will cause that area to be attacked by trials so that we can see. He is increasing our faith so that we might be at peace and trust Him. He pushes us beyond our means so that we will get to know Him for who He is. He is not trying to stop people from dying; He is trying to show that He is not only the Lord of the living but the Lord of the dead. We can entrust Him with all things.