I'm not a lawyer or accountant, but here is my two cents. The answer to your question is basically dependent on what your mortgage paperwork says. It is a recourse or non recourse loan? If it is the first, then yes, they can come after other personal assets. If it is the latter, then they cannot.
In Arizona non-recourse loans are the standard. I'm assuming since your property is in Marana (my backyard), your loan was originated here. If not, check your state's standard, and then your loan paperwork.
Secondly, your question regarding Aurora being willing to 'settle' on the difference owed. Answer: Maybe. Give them a call and see what you can work out. I've had several clients who were considering short sales who were able to work a deal with the bank and not have their credit affected.