Easier to notify, than get signatures.

Automatic Rejection: Your application will be automatically rejected for any of the following:a) Eviction by a prior landlord in the last 24 months;b) Outstanding debt or unpaid damages to a previous landlord;c) Undisclosed criminal record, felony or misdemeanor;d) Being registered as a sex offender;e) Conviction of possession or distribution of a controlled substance;f) Conviction of spousal abuse or violent crime;g) Currently pending the outcome of a felony or misdemeanor charge;h) Bankruptcy in the past 5 years that has not been discharged/released;i) Invalid social security number;j) Outstanding federal tax lien, the repayment terms for which are not current;k) False information on your application;l) Incomplete application, including applicant signature on all pages of the application and this form;m) Failure to pay the application fee at the time of application submittal.

It's a European design signature.

Never send anything requiring a signature. 

When you set up a maintenance inspection, explain that you will be bringing a new agreement to get new signatures.  

If you must require a signature and she just refuses to sign, you can give her proper notice and simply not renew the lease

Next time, also get estoppels with the seller and tenant signatures so you're all on the same page about when rents are due, how much they are, and how much security deposits are owed.Take it as bitter medicine.  

Its not so much about the signature in this case rather than papering the file to show the courts (if needed) that the landlord was responsive to the tenants concern with a reasonable solution to protect them. 

When I execute a lease, the only way my signature gets on that document and the only way the keys get turned over is when I have all monies.

I'm tired.And I'd make their new lease contingent on the signature of the departing tenant agreeing to terminate and duke it out with the other tenants, regarding any refund of their portion of the security deposit.Your lease agreement time frames are odd.