The pathway I am most familiar with involves necrosis and apoptosis. The signaling messenger is calcium ions. In this pathway, the breakdown of the mitochondria results in massive ROS generation and leakage. The calcium can trigger other cells to do the same. This at least occurs in metazoic eukaryotes. I am not sure about yeast though, since they are unicellular. I recommend a literature search because eukaryotes can sometimes be very different depending on whether they are multicellular. That stated, sometimes they are the same due to conservation.
Basic biochemistry has shown that electron transport processes in chloroplasts and mitochondria (and else where in cells) result in generation of different reactive oxygen species (ROS) which then interact with cellular components. The cell has mechanism s for detoxifying ROS. When the normal metabolism functions, the detoxification is adequate so minimizing damage . If ROS production exceeds the capacity to detoxify then damage ensues. An example is in plant cells, where light absorption by chloroplasts is potentially often in excess of the capacity to detoxify especially when CO2 supply is limiting when water is limiting and stomata close. This leads to very rapid inhibition of Coupling Factor in the chloroplast and decreased ATP synthesis , which then has further profound effects on photosynthetic CO2 assimilation and many other cellular processes. Please see
Plant, Cell and Environment (2002) 25, 275–294 Photosynthetic carbon assimilation and associated metabolism in relation to water deficits in higher plants D. W. LAWLOR & G. CORNIC
I prefer not to think of this or many of the ROS related processes as a signalling mechanism or stress sensor because it is moreto do with basic metabolism.