From what I gather people sometimes may devise fake proof of income to be granted loans -- loans they don't expect to pay back anytime soon or in some cases ever.
It's probably very easy to fake proof of income in digital documents. Lenders may only consider bank statements or taxes and that can all easily be faked as well. Given that you lied about income, when or why would it be a crime in the case of obtaining a loan vs. just lying about it in general?
I doubt there's a specific, particular law that states lying about income to obtain income is illegal.
Fraud is a very gray area kind of criminal act -- often it's excessively hard or impossible to define it.
In such an example, a person may get a $100,000.00 loan when they make $9,000/year through the deception. I assume, if you can pay any of it back at any rate, you'd have no reason to be in trouble.
But how might it really go down?
As an example, a friend needs some fast money to go to Canada, but he in no way can get $6,000 he needs for what he plans to do in just 5 days. His plan? Lie about income and obtain that amount from a lender, with intention to pay back -- just probably not within the means/rate/amount the lender may establish. So he does intend to pay back -- just wants to use deception to convince the lender that he has the capability/income to pay that amount back when he doesn't as of right now.