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As a general rule if a property is not ADA accessible, the owner doesn't have to remodel it to meet current code unless they are actually doing construction projects that require them to pull a permit. Then they have to comply with all applicable code requirements including ADA rules.
But if there are no handrails at all, that sounds like a code violation all by itself and you can call the local Code Enforcement office or Housing Inspector and they can come out and cite the owner if the property is not up to code. In most situations with stairs, at least one handrail is mandatory on a set of stairs...