Intestate individuals have executors appointed by the court who organize and present a list of assets and debts to the court. The court then decides how to divide the assets according to law. If a person dies destitute the county is forced to pick up the burial costs. Most of these people, end up in paupers graves. In larger jurisdictions, they are often buried en masse.
Counties generally keep separate indexes to their probates and wills.
They are available on a local basis. Many of the probate records are available through the Utah Genealogical Society library in Salt Lake City, Utah.