According to one bank with whom I work, the lenders have the option of approving the loan even if there isn`t sufficient back-up collateral under the SBA Express program which covers amounts up to $350 thousand.
But the loans I wrote about in Unique Business Loans for Minorities are not SBA loans. As I wrote "Generally, the borrower must pledge sufficient assets, to the extent they are reasonably available, to secure the business loan." As in most loans, the underwriting criterion vary and each lender will base a decision on the unique facts of the lending opportunity.