If you are able to get the promise in writing that will be helpful. If not, you can still pursue the verbal promise. It's just harder.
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You already have her promise to pay the rent in the lease you both signed with the landlord. You are not damaged until you pay all the rent remaining on the lease without her contribution. She will have a defense based on the fact that even though she moved out leaving you with the entire burden, you also made a promise to pay the rent to the landlord in full. Her promise to pay the rent is independent of your promise to pay the rent to the landlord in full, and you had the benefit of use of the entire leasehold to yourself in her absence.
As of now, she does not owe anything to you. I doubt that you will freely obtain a confession of judgment from her, but if she agrees to confess to the debt, make certain that you engage an attorney to prepare the agreement. You would only enforce that confession or promissory note, if she does not pay.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
It would be most beneficial to you if you had it in writing that she agreed to pay 1/2 the rent to you. As it stands, since both of you signed the lease you are each obligated to pay the rent in full to the landlord. Since you are the only one living there you have the entire benefit of occupancy and therefore a court may not award damages to you. If, on the other hand, you were to stop paying the rent the landlord could look to both or either of you for the rental payment.
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