The Invar anomaly is one of the most fascinating phenomena observed in magnetically ordered materials. Invariant thermal expansion and elastic properties have attracted substantial scientific attention and led to important technological solutions. By studying planar faults in the high-temperature magnetically disordered state of Ni1-cFec, here we disclose a completely different anomaly. An invariant plastic deformation mechanism is characterized by an unchanged stacking fault energy with temperature within wide concentration and temperature ranges. This anomaly emerges from the competing stability between the face-centered cubic and hexagonal close-packed structures and occurs in other paramagnetic or nonmagnetic systems whenever the structural balance exists. The present findings create a platform for tailoring high-temperature properties of technologically relevant materials toward plastic stability at elevated temperatures.