During the endgame of elimination programs, parasite populations may exhibit dynamical phenomena not typical of endemic disease. Particularly, monitoring programs for tracking infection prevalence may be hampered by overall rarity, the sporadic and unpredictable timing and location of outbreaks, and under-reporting. A particularly important problem for monitoring is determining the distance that must be covered to achieve the elimination threshold at an effective reproduction number less than one. In this perspective, we suggest that this problem may be overcome by measuring critical slowing down. Critical slowing down is a phenomenon exhibited by nonlinear dynamical systems in the vicinity of a critical threshold. In infectious disease dynamics, critical slowing down is expressed as an increase in the coefficient of variation and other properties of the fluctuations in the number of cases. In simulations, we show the coefficient of variation to be insensitive to under-reporting error and therefore a robust measurement of the approach to elimination. Additionally, we show that there is an inevitable delay between the time at which the effective reproduction number is reduced to below one and complete elimination is achieved. We urge that monitoring programs include dynamical properties such as critical slowing down in their metrics for measuring achievement and avoid withdrawing control activities prematurely.