It has nothing to do with poor or rich.  It applies to both equally.

Residency is verified through something like E-verify.  Once a year, every adult in the state has to verify their residency status.  (The technology exists to do this through a secure website.)  No current verification, no monthly rebate check.  In other words, this works within the existing system (which means that we won't be firing everyone from the state's Department of Revenue).

I forget the exact mechanism, but there is a way for companies to collect and transmit sales tax across state lines for online purchases now.  As an example, I regularly do business online with a company headquartered in Florida, and every time I make a purchase the Michigan sales tax is right there in my receipt.

The prebate structure is pretty simple:  Take the current federal poverty line, multiply it by the FairTax rate (0.0975 for the MFTP), and then divide that result by 12.  For a single adult resident of Michigan, that works out to about $88.48 monthly.