So if I understand correctly, the Chandrasekhar limit (\sim 1.4 \ M_{\odot}) is the maximum mass that a white dwarf can have. Beyond this mass, the degeneracy pressure of the electrons can no longer sustain gravity, and the star collapses. However, I personally find difficulties in applying this limit to generic stars and to make a connection with supernovas.
The only situation that I perfectly understand is when a white dwarf of small mass is already formed, and then it starts accreting mass from a companion star. When the mass of the white dwarf goes above 1.4 \ M_{\odot}, a supernovae of type Ia is formed.
But can we apply the Chandrasekhar to other generic stars that have still not become white dwarfs? For example, knowing that our sun has 1 \ M_{\odot}, can we ensure it will become a white dwarf? I think in this case another limit should be applied (of around \sim 8 \ M_{\odot} ), but I don't understand its relation with the Chandrasekhar limit.
Above I described a situation in which a white dwarf is the stage before a supernova. But are there other situations in which a white dwarf is tha stage after a supernova? If yes, which types of supernova?
Thanks in advance.