Minnesota is a Non-recourse state, so if you only have 1 mortgage they can not pursue you after a foreclosure for a deficiency.
Where this changes is for 2nd mortgages and multiple liens. They do have a legal right to pursue a homeowner through a judgement.
I have pasted a link to my blog that talks about this topic more in depth. In my opinion those with multiple mortgages & HELOC's are the best candidates for short sales. If you would like to speak with me directly just contact me directly on Trulia!