You may be able to collect rent until you re-rent the place, if your state has a law covering the effect of a delivered but unsigned lease. If not, you had a month-to-month lease, & T had to give proper notice & is still on the hook for July rent. Your damages include the stopped check fees, costs of new locks, costs of informing the utility companies that she left & they might want to shut off the power/water, attorney fees, & costs.
You can find out her new address by mailing her an empty envelope with "Do Not Forward, Address Correction Requested" written in red on the envelope. The PO will slap the forwarding address sticker on & send the envelope back to you. Then you know where to send the process servers.
Sue her in small claims court, then garnish her wages/put a lien on her car to force her to pay. She's about to pay some tuition to the university of life!
If you post your state, we'll look up the laws for you....
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.