"Every person who, knowing that any book, paper, record,
instrument in writing, or other matter or thing, is about to be produced in evidence upon any trial, inquiry, or investigation whatever, authorized by law, willfully destroys or conceals the same, with intent thereby to prevent it from being produced, is guilty of a misdemeanor." (Cal. Pen. Code. S. 135)
What if the paperwork in question isn't being used in an investigation, but rather as a way of proving residence in a particular area for the purpose of receiving services provided in that area?
Pretty sure that the laws of all 50 states considers that to be fraud.
If the person committing the fraud is poor however or very young, the will to prosecute the fraud is often absent, but you cannot count on that.
For example, someone was prosecuted here in California for helping a friend without health insurance obtain medical care by trying to get the hospital to believe that his friend was him.