Zero returns are an attempt to get money back from the IRS after filing. The process involves filing a tax return with the IRS which shows zero income.
This method is advocated by Pete Hendrickson, notably in his book “Cracking The Code” and on his website, Lost Horizons. Both Pete Hendrickson and his wife, Doreen, were sentenced to prison after using this method. (Source.)
They may work to get money back from the IRS, but are not recommended by Freedom Law School because it defeats the purpose of not filing, and involves lying on a return which exponentially increases your chances of being pursued by the IRS.