In contrast to predictions of conventional epidemic models, COVID-19 outbreak time series have highly asymmetric shapes, with cases and fatalities declining much more slowly than they rose. Here, we investigate how awareness-driven behavior modulates epidemic shape. We find that short-term awareness of fatalities leads to emergent plateaus, persistent shoulder-like dynamics, and lag-driven oscillations in an SEIR-like model. However, a joint analysis of fatalities and mobility data suggests that populations relaxed mobility restrictions prior to fatality peaks, in contrast to model predictions. We show that incorporating fatigue and long-term behavior change can explain this phenomenon, shed light on when post-peak dynamics are likely to lead to a resurgence of cases or to sustained declines, and inform public health campaigns to control COVID-19.