An authority shall make periodic investigations of each family admitted to a low-rent housing project and, on the basis of the investigations, shall determine whether that family at the time of its admission (1) lived in an unsafe, unsanitary, or overcrowded dwelling or had been displaced by a project or by off-site elimination in compliance with the equivalent elimination requirement hereof, or actually was without housing, or was about to be without housing as a result of a court order of eviction, due to causes other than the fault of the tenant, and (2) had a net family income not exceeding the income limits for admission of families of low income to the housing; provided that the requirement in clause (1) shall not be applicable in the case of the family of any veteran who has been discharged, other than dishonorably, from, or the family of any service person who died in, the armed forces of the United States, if that family had made application for admission to the project within any time limit specified by federal law applicable to federal financial assistance for the project. If it is found upon investigation that the net income of any families have increased beyond the maximum income limits fixed pursuant to section 469.022 for continued occupancy in the housing, those families shall be required to move from the project.