Protecting Our Students and Taxpayers Act of 2019 or the POST Act of 2019 This bill modifies requirements for a proprietary (i.e., for-profit) institution of higher education (IHE) to participate in federal student aid programs. Current law requires a proprietary IHE to derive at least 10% of its revenue from sources other than federal student aid. This bill requires a proprietary IHE to derive at least 15% of its revenue from sources other than federal funds (i.e., it replaces the so-called 90/10 rule with an 85/15 rule). Additionally, the bill limits what a proprietary institution may treat as revenue to the school in calculating whether it derives at least 15% of its revenue from sources other than federal funds. Finally, the bill makes compliance with the 85/15 rule a condition of institutional eligibility to participate in federal student aid programs (i.e., failure to comply results in immediate loss of institutional eligibility). Currently, a proprietary IHE must violate the rule for two consecutive years before losing eligibility.