Trying to keep my deposit.

New to renting and this is a room I'm renting not an apartment. Also definitely might be the wrong place to ask for legal advice but my landlord is asking me to stay an additional 15 days to give her 1 month's time to find a new tenant. My rent ends at the end of this month and I was told I will be paying for the 15 additonal days starting next month continuing my rent out of my free will. I signed no lease agreement but she's threatening to keep my deposit if I don't follow through with her 30 day notice. All she gave me was a rental guide paper on what her rules are and I signed previous paper work to allow a background check on me? She said there's no lease agreement and said I only got a guide.