I personally do not know a single investor who has been sued and had a judgement for anything greater than what a basic insurance policy can over, so i do not subscribe to the paranoia but I do use basic structure and separation of assets for protection.

And the original borrower may have a deficiency judgement on them for the first bank to recover that loss.

You will lose the last months rent which you may or may not be able to get a small claims judgement against her for.

I know the 1st deal is always the hardest and most scary, but once you have gone through a couple it becomes routine and in my experience you just hope nothing un-expected pops up - like mortgages, liens, judgements, etc - which seems to happen A LOT.  

You don't need a lawyer for small claims, document everything you can and get a judgement...ask for the max, don't discount anything. $3400 sounds low for all that.

I want to offer on a property that I've found but the owner has said that she will take offers that allow her to stay in the property for another month or two into greater consideration than offers that don't.She's a sick elderly woman and she has a judgement for 60k pending foreclosure sale in November.

You likely won't get any money, but you might get a judgement against them. 

If you define it as getting a judgement that is collectable, I'd say probably not.

Without being judgemental, the people that frequent the place have face, neck and prison tats.

This is very simple.You file eviction.Go to court.When you stand in front of the judge present the facts.Be emotionless when you speak and have timeline in a clear,concise,and quick manner.The judge listens to all kind of long BS all day long and when they get someone who keeps quiet and gives and quick and concise response you will stand in good favor with them.I usually let the tenant dig a big hole for themselves and it works every time.The less you can say is better.The judge has heard every excuse before and will quickly dispose of the tenant.Usually after the judgement is entered you can pay for a writ where the marshall will come and throw the tenants stuff out.Depending on how many writs they need to serve that month it could take 3 to 4 weeks to get them out.The tenants do not know the writ office is back up so most leave right away.Here if 500 or less of property is left and it appears they have abandoned the property you can re-key and throw the stuff out.Here if they do not file an answer in Georgia for the court you can get the writ but not a judgement.I would have to pursue them in small claims court then.So as you can see it is vary important to learn processes for your state.I condition tenants before they sign a lease.No drugs,smoking inside,sex offenders,felons,aggressive dogs,etc. will be tolerated.We do inspections once a month and if ANY lease provision is violated we evict immediately.Everyone of my tenants pays on time now and the others have left.It's kind of like having a slack employee trying to get away with stuff all the time versus a great employee that works hard.