It's like prayer cloths. I believe that the Scriptures clearly imply a transfer of power or anointing on the cloth. Let's read the text together...
Acts 19:11-12 (ESV)
11 And God was doing extraordinary miracles by the hands of Paul, 12 so that even handkerchiefs or aprons that had touched his skin were carried away to the sick, and their diseases left them and the evil spirits came out of them.
Notice the emphasis of having touched Paul's skin. Also note the explanation of "extraordinary miracles". That word, "extra-ordinary", meaning, "beyond the ordinary". These were beyond the ordinary miracles that had been recorded or seen. After having touched Paul's skin, these handkerchiefs were embued with the very power of God. I do not doubt that a seeker could have placed one of these cloths on a comatose man and the man be healed. It had to do with the fact that it had touched Paul's skin, it wasn't predicated on any prayer or faith on behalf of the receivers. It was a demonstration of power, not necessarily faith or agreement.
It's like Elisha's bones. Let's read that text also...
2 Kings 13:20-21 (ESV)
20 So Elisha died, and they buried him. Now bands of Moabites used to invade the land in the spring of the year. 21 And as a man was being buried, behold, a marauding band was seen and the man was thrown into the grave of Elisha, and as soon as the man touched the bones of Elisha, he revived and stood on his feet.
Please note, nobody was praying or standing in agreement for this man to be raised from the dead. In fact, the man was hurriedly thrown into the grave of Elisha so that those burying him could flee. Upon merely "touching" (remember the emphasis on the prayer cloths discussed about having touched Paul's skin)... upon merely "touching" the bones of Elisha. Please note, Elisha had been dead roughly a year. There was clearly a transference of healing power that moved on account of physical contact. No prayer or agreement necessary.
The very same principle at work in the residual power within Elisha's bones is the very same principle at work in the residual power found in prayer cloths, anointed oil, and blessed elements or items.