There are Orphanages in Japan but they are well hidden. In Japanese culture that is obsessed with avoiding shame, birth parents and the orphans themselves would rather prefer NOT to be well advertised of their (what they consider to be a shameful) status. In old days, these were virtually unknown to common people.
Today, just type in "Japan Orphanage" in Yahoo, you can get quite a list.
By the way, if you walk down the streets of Japan, you almost never see people in wheel-chairs or meet people who are mentally challenged. That doesn't mean these people do not exist. Society in general marginalize these people so much that they rarely come in public view, except for the brave few. (I have personally known a few)
Japan has a very structured society. Anyone who doesn't belong in narrowly defined "norm" tend to disappear altogether.