Tenant leaving but can't pay last 2 months rent, payment plan?

[Madison Balter]

My tenant has been applying for section 8 starting in June, got accepted but for a unit that doesn't qualify for mine. She told me that if the voucher qualified then section 8 would pay the rent for June, July and now August. However my tenant needs to move and stated in writing she will be out by the 1st of September. She verbally agreed to creating a payment plan to pay me back the rent for June, July and August. Is this legal? Can I go about creating a legal document that can hold her responsible for that lost rent? I know I could keep her security deposit for the lost rent which covers 1 months rent. I'm feeling lost. Does anybody have other ideas for other options. My tenant is willing to work with me but I also realize I may never see that rent money and have to call it a loss. Thanks!