Final answer:
A star ends its evolutionary life and becomes a white dwarf when it ceases all nuclear fusion, stabilizes due to degeneracy pressure, and has a remnant mass below the Chandrasekhar limit of about 1.4 solar masses.
Step-by-step explanation:
The event that marks the end of a star's evolutionary life before becoming a white dwarf is the cessation of all nuclear fusion reactions in the star's core. As the star sheds its outer layers and loses mass, it becomes stabilized by degeneracy pressure exerted by electrons. If a star's remnant mass is below the Chandrasekhar limit, which is approximately 1.4 times the mass of the Sun, it will not collapse further and will ultimately cool to become a white dwarf. Over time, without any fusion reactions in their cores, white dwarfs will emit their remaining heat into space and cool down to become black dwarfs, which are mostly composed of carbon, oxygen, and neon.