I am also in this category, and so are many others. We hope to get loans, scholarships or some other means to fund our education overseas. Thing is, he should have applied to some moderate and safe schools as well. LOR is also a thing too. Candidates who write LORs themselves can submit applications to as many schools as possible but it's difficult to ask a professor to submit LOR to say 8 schools. Except if you are hoping they'd send something generic.
@demoralizer you can still apply to some schools...I'd encouraged you apply to one or two more schools, perhaps NYU, NCSU or Chicago. Chicago and NYU can waive the application fee if you send them a mail or attend any of the info sessions. Check when the round 2 deadline is and try to apply.
For the LOR, you have to summon courage and ask them for help. It's better you secure an admit this year in a school of your choice than to come back next year asking them for the same thing. Paying them a visit to explain your situation (if you can) might also help.
Best.