Legal Question in Landlord & Tenant Law in Illinois

Without a written lease there is nothing to 'prove' that the landlord had agreed to clean up or fix anything before, or after, move-in. Normally to cancel a month-to-month lease you have to give notice on the same date that rent is due, normally the first of the month. If the lease is in writing even though it is "month-to-month" you need to check to see if it required some other notice. From a factual standpoint, the problem here is that it is one thing to give a deposit on promise that a place will be fit on move-in; it's another to move-in even if the place is not as promised -- makes it seem as though it wasn't the landlord's obligation. Check in your town however if there is a landlord-tenant ordinance that imposes requirements on the landlord. If the place was that filthy, and apart from your daughter selecting such a place, a complaint to the local building department may also prove helpful. But without a lawyer who understands all of the facts, and some are missing, you and your daughter are at risk for losing the deposit and potentially a couple months rent. Good luck.