The limit is the point where Gravity overcomes Electron Degeneracy pressure. Its current estimate is 1.44 solar masses. Such a limit was first calculated in 1929 and 1930, first by E.C. Stoner and Wilhelm Anderson, and later was refined by Subrahmanyan Chandrasekhar.
Stars losing their thermonuclear-generated heat and pressure that are sufficiently massive that after ejecting mass they remain above this limit collapse into neutron stars or Black Holes. White dwarfs accreting matter can reach this limit and collapse as well. Some of these collapses result in various types of supernovae.
The analogous limit above which an object must collapse into a black hole is the Tolman-Oppenheimer-Volkoff Limit.
Tolman-Oppenheimer-Volkoff Limit (TOV)