When a galaxy loses cold gas, thus suppressing star formation
In astronomy, quenching is the process in which star formation shuts down in a galaxy. A galaxy that has been quenched (with little active star formation) is called a quiescent galaxy. Several possible astrophysical mechanisms have been proposed that could lead to quenching, which either result in a lack of cold molecular gas, or a decrease in how efficiently stars can form from molecular gas. 
Quenching mechanisms.
Active supermassive black holes.
Evidence suggests that active supermassive black holes may drive quenching. The strong jets of some active supermassive black holes may heat up cold gas, thus suppressing star formation. 
Environmental quenching.
Several proposed galaxy quenching mechanisms rely on the environment a galaxy is situated in. One example of this is when a galaxy passes through a dense intracluster or intergalactic medium. The motion of the galaxy through this medium creates a ram pressure force which can strip gas away from the galaxy. Through this mechanism, known as ram pressure stripping, galaxies can be depleted of gas.
Galaxy Mergers.
Inflows of gas from galaxy mergers can activate supermassive black holes within galaxies, thereby resulting in quenching via feedback from active galactic nuclei jets. Merger events can also trigger rapid bursts of star formation. This rapid star formation can lead to high rates of events like supernovae, which disrupt cold gas. This quenched state is sometimes called a post-starburst galaxy.
Morphological quenching.
In morphological quenching, a galaxy’s evolution from a disk to a spheroid can reduce the efficiency of star formation over time, leading to lowered rates of star formation.
Reionization.
In the Epoch of Reionization, the first generation of stars heated gas throughout the universe. This process is thought to have quenched some smaller dwarf galaxies with small cold gas reservoirs.
Quenching and galaxy evolution.
The process of quenching is connected to the observed dichotomy between massive galaxies of red elliptical galaxies, which have little active star formation, and blue spiral galaxies, with active star formation. One common evolutionary path on the galaxy color–magnitude diagram may start with a blue spiral galaxy with much star formation. The black hole at its center may start growing rapidly, and somehow start quenching the galaxy, which relatively quickly transitions through the "green valley", ending up more red.
References.
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