Mortgages for Japanese residents without citizenship or permanent residency
If you live in Japan and want to get a mortgage to buy a home, most banks require either citizenship or permanent residency. Shinsei Bank will make an exception if your spouse is a Japanese citizen or permanent residence. Another group of banks don't require any of the above.
Here are the Japanese lenders I've found that do not require citizenship, permanent residency, or a Japanese spouse. Where only some of the bank's loan products are available to non-permanent residents, I've called out the name of the applicable product(s).
Tokyo Star Bank - Star Home Loan
Detailed requirements are listed on the 商品説明書 (Product Manual) tab
SBJ Bank (Shinhan Bank Japan) - ANY Home Loan / ANY Home Loan Plus
FAQ stating that you do not need permanent residency to apply for a loan. Sounds more non-committal than some of the others.
This page implies they may offer loans to people living in Japan without permanent residency. However, detailed requirements are not spelled out. The one-pager (PDF) for their My Home 100 loan actually lists Japanese citizenship or permanent residence as a requirement, so perhaps they make exceptions on a case-by-case basis.
Note that I have no experience actually trying to get a mortgage from any of these lenders. The information is provided as-is without endorsement or guarantee.