Abstract Unless they adapt, populations facing persistent stress are threatened by extinction. Theoretically, populations facing stress can react by either disruption, increasing trait variation, or stabilisation, decreasing trait variation. In the short term, the more economical response is stabilisation, because it quickly transfers a large part of the population closer to a new ecological optimum. However, canalisation is deleterious in the face of persistently increasing stress because it reduces variability and thus decreases the ability to react to further change in stress. 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 adaptive reaction of populations facing extinction are rare. In this study, 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 variance in two species across a salinity rise leading to their local extinction. One species reacted by stabilisation in shape and size, detectable several thousand years prior to extinction. The second species reacted by trait divergence, but each of the two divergent populations remains stable or reacted by further stabilisation. These observations indicate that the default reaction of the studied Foraminifera is stabilisation and that stress escalation did not lead to the local emergence of adapted forms. Inability to breach the global adaptive threshold would explain why communities of Foraminifera, and many other groups of marine plankton, reacted to Quaternary climate change by faithfully tracking their zonally shifting environments. It also means that populations of marine species adapted to response by migration, when exposed to stress outside of the adaptive range, will be at risk of extinction.