Unless they adapt, populations facing persistent stress are threatened by extinction. Theoretically, populations facing stress can react by either disruption (increasing trait variation and potentially generating new traits) or stabilization (decreasing trait variation). In the short term, stabilization is more economical, because it quickly transfers a large part of the population closer to a new ecological optimum. However, stabilization is deleterious in the face of persistently increasing stress, because it reduces variability and thus decreases the ability to react to further changes. Understanding how natural populations react to intensifying stress reaching terminal levels is key to assessing their resilience to environmental change such as that caused by global warming. Because extinctions are hard to predict, observational data on the adaptation of populations facing extinction are rare. Here, we make use of the glacial salinity rise in the Red Sea as a natural experiment allowing us to analyse the reaction of planktonic Foraminifera to stress escalation in the geological past. We analyse morphological trait state and variation in two species across a salinity rise leading to their local extinction. Trilobatus sacculifer reacted by stabilization in shape and size, detectable several thousand years prior to extinction. Orbulina universa reacted by trait divergence, but each of the two divergent populations remained stable or reacted by further stabilization. These observations indicate that the default reaction of the studied Foraminifera is stabilization, and that stress escalation did not lead to the emergence of adapted forms. An inherent inability to breach the global adaptive threshold would explain why communities of Foraminifera and other marine protists reacted to Quaternary climate change by tracking their zonally shifting environments. It also means that populations of marine plankton species adapted to response by migration will be at risk of extinction when exposed to stress outside of the adaptive range.