Immigrants, farmers without their own land, single women, and former slaves could all qualify. The fundamental racial qualification was that one had to be a citizen, or have filed a declaration of intention to become a citizen, and so the qualification changed over the years with the varying legal qualifications for citizenship. African-Americans became qualified with the passage of the Fourteenth Amendment in 1868. South Asians and East Asians who had been born in the United States became qualified with the decision of United States v. Wong Kim Ark in 1898, but little high-quality land remained available by that time. For immigrants the fundamental qualification was that they had to be permitted to enter the country (which was usually co-extensive with being allowed to file a declaration of intention to become a citizen). During the 1800s, the bulk of immigrants were from Europe, with immigrants from South Asia and East Asia being largely excluded, and (voluntary) immigrants from Africa were permitted but uncommon.
While home ownership has historically been considered a hallmark of the American Dream, financial distress and bankruptcy can reverse fortunes rather quickly. Fortunately, all states have laws intended to help struggling homeowners keep their primary residence when seeking bankruptcy protection.