Given the complexity of your parentsÂ’ problems, and the numerous programs and agencies potentially involved in any solution, a knowledgeable social worker whose profession requires that he/she stay current on all available benefits programs for the elderly, disabled and indigent, should be able to help. I do not know your state or county, but I believe all welfare programs are run through each state government and administered at the county level by the local county welfare office. There should be a department listed as a sub-unit in your directory as, "Adult Protective Services" or something similar. I believe your parents would qualify for services since they do not have a home and are advanced in years and disabled. The social worker will advise you on what is available so that you can help your parents with a suitable choice within their income limitations.
Any collateral needs should be discussed with the social worker, such as mobility aids or other medical needs. The social worker can interface with Social Security Administration on the issue of whether your mother would qualify for disability assistance if she is not already receiving her social security retirement. She should already be on Medicare, but the social worker can help straighten out any kinks, if any. Your contact at the welfare office should become your resource for your parents' future needs. It would be a logical place to start your search anytime such issues recur.
You can start your search for assistance by visiting the National Adult Protective Services Association website. I wish your parents the best of luck in finding suitable accommodations, and hope that the information I have provided helps you Find. Learn. Save.