Question: Lets say you work in Chicago and live in Chicago but put your home address as somewhere in Indiana. Then every week you collect the mail that is being sent to you in Indiana. Wouldn't you save a lot of money assuming the taxes are lower? What prevents people from doing this?

Answer: 
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> What prevents people from doing this?
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* Laws (if you are *lying* about your residency)
* Convenience
* It won't work for income taxes

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> Wouldn't you save a lot of money assuming the taxes are lower?
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According to the [Illinois Department of Revenue](https://www2.illinois.gov/rev/individuals/filingrequirements/Pages/default.aspx):

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> you must file Form IL-1040 and Schedule NR if
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> * you earned enough taxable income from Illinois sources to have a tax liability
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So just *claiming* you live in Indiana won't stop you from owing income tax in Illinois. Plus Indiana might compensate for lower income taxes with higher property taxes, so you might actually may *more* taxes with this scheme.

(I see in the comments you only want to create a PO Box, so this may not apply, but it does apply to other situations where people *legitimately* live across state lines).

NBA players actually have to pay tax to [*all states that they play in*](https://www.slamonline.com/nba/state-taxes-nba-free-agency/). Otherwise, every player would move to a state that has no state income tax.
According to [the Illinois Department of Revenue](https://www2.illinois.gov/rev/questionsandanswers/Pages/10.aspx), you must file an Illinois income tax return if “you earned enough taxable income from Illinois sources to have a tax liability[.]” There is a form for residents of Iowa, Kentucky, Michigan or Wisconsin to fill out exempting them from withholding, but not Indiana. “If you received wages, salaries, tips, and commissions from Illinois employers, you are not required to pay Illinois Income Tax on this income. This is based on reciprocal agreements between Illinois and these states.”

So this might be useful if you earn a lot of passive income from investments out-of-state (although in that case the way to make them tax-free *legally* is to buy muni bonds), or if you want to work in Indiana but live in Chicago, but not if you work and live in Illinois.

Most people who work in Illinois would have state income tax withheld, although the hypothetical tax cheat would have several ways around that.