I'm often approached by people who say they want a will so their property doesn't go to the government. While there's many reasons to have a will (probably a smoother probate and smoother family relations is just one of many reasons), the risk of having the government "take" your stuff merely because you don't have a will is very unusual. So, what happens when there is no will?
When someone dies without a will, it's stated that the individual died "intestate". All states, including Minnesota, have intestacy laws which give a specific order as to who gets how much of the estate. In general terms, a spouse gets first. If there's no spouse, then the children get and so forth. If the decedent died without a spouse or descendants, the parents get first and if no parents, the siblings get and so forth. If there is no spouse or descendants, parents or siblings, then the grandparents get or aunts and uncles if no grandparents and so forth. The main point is that the state of Minnesota is the last resort. If there are no relatives around to claim the estate, only then does the estate go, or escheat, to Minnesota.
There are many reasons to have a will, but probably one of the most minor reasons is to prevent Minnesota from getting your stuff.