So basically I'm at risk of the tenant damaging my property and not having a way of going after her because she is not signed to the lease. 

They did not make an offer to pay rent/damages/legal fees before the deadline of the eviction. 

As far as the SD, disperse it as usual...apply any damages and refund the remainder.

For example, California has a TDS and SPQ, basically tells the buyer exactly what is going on with the house, and the seller needs to disclose or the buyer can come after them for damages.. 

Any damages  a tenant must pay for, unless its an act of nature or tree roots. 

The real estate market is not a very efficient market, it is heavily influenced by deeply human factors.

You are obligated to make a good faith effort to find a replacement tenant and minimize the damages to your departing tenant.

Having a detailed rehab plan and experienced team is critical.Not Screening Tenants Properly:The rental phase is crucial, and bad tenants can cause property damage or miss rent payments, disrupting your cash flow.

@Renee CossRecommend you first figure out the property Class you want to invest in, THEN figure out the corresponding location to invest in.Property Class will typically dictate the Class of tenant you get, which greatly IMPACTS rental income stability and property maintenance/damage by tenants.If you apply Class A assumptions to a Class B or C purchase, your expectations won’t be met and it may be a financial disaster.If you buy/renovate a Class A property in Class D area, what quality of tenant will you get?

@Kelsey Vander Meulen unless you have a great team lined up, especially someone who can address a burst pipe or damaged roof late night or on a Sunday, hire management.