Home financing for Non-Citizens or limited credit borrowers.

Not my bank. Not an endorsement. That said, at least someone is trying hard to grow their share of this market:

https://www.bankofthewest.com/personal-banking/international-clients.html#your-products

If anyone happens to get more data on this (rate/LTV, etc) post here please.

My .02c

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Lawful resident non-citizens can borrow on the same terms as citizens--that much is nothing new. For conforming loans, there was a Freddie Mac bulletin on the lack of a credit score angle recently.

Here it is:
http://www.freddiemac.com/singlefamily/guide/bulletins/pdf/bll1702.pdf