They should not worry as residing legally in low income apartments on merits is not a crime. They should submit the affidavits stating the truthful corroboration of your residency there for the cited time periods on factual evidence.
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From the immigration perspective, this is not a problem.
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.