Biological control systems regulate the behavior of biological systems in a constantly changing environment. Homeostasis is the most widely studied outcome of biological control systems. Homeostatic systems maintain the system in its desired state despite variations in system parameters or the externally-determined input rates of their constituents, i.e. they have zero or near zero steady state error. On the other hand, allostatic systems are not resistant against environmental changes and the steady state level of their controlled variables responds positively to the changes in their input rates. Little is known, however, on the existence and frequency of reverse allostatic systems, where the steady state value of the controlled variable correlates negatively with the input rate of that variable. In the present study, we derive the minimal conditions for the existence and local stability of reverse allostatic systems, and demonstrate in examples of metabolic, pharmacological, pathophysiological and ecological systems that the reverse allostasis requirements are relatively non-stringent and may be satisfied in biological systems more commonly than usually thought. The possible existence of reverse allostatic systems in nature and their counter-intuitive implications in physiological systems, drug treatment, ecosystem management, and biological control are explored and testable predictions are made.