Inherited tenant security deposit

[Nevin Rasor]

I recently purchased my first duplex and inherited one of the tenants until October(when her lease ends). She is well below market rent and attempts to amend her lease up to appropriate rent have been unsuccessful.
The dilemma I have now is the security deposit. I have not received a walk-in inspection from the seller for this tenants unit, so I am assuming it was not done. I know there are some significant repairs that will need to be done after the tenant moves out, but I noticed them when I looked at the house to purchase it. 
My original thoughts were to delegate the security deposits towards any issues that are not normal wear and tear. However, the tenant wants to do a walk-in inspection because of the change in ownership. I don't agree with this, as it doesn't accurately represent the previous 11 years she has been a tenant there. 
I want to handle this correctly from a legal standpoint but also not be taken advantage of. Thanks in advance for your thoughts and advice.