According to this post, I found that about 90% of all stars are main sequence stars. So I am assuming that the other 10% consists of protostars, older giant stars, and stellar remnants. So I'm wondering how much of the stellar population is dead (i.e. turned into a remnant, excluding supernova progenitors that blow apart the whole star without leaving anything behind)?
Most of the remnants are white dwarfs, because their progenitors can be much shorter lived than the lifetime of the galaxy and are much more numerous than the higher mass progenitors of neutron stars and black holes.
A census of the local neighborhood suggests that about 10% of "stars" are white dwarfs. This number is low because (a) only stars more massive than about $1M_\odot$ have had time to become white dwarfs and (b) the birth stellar mass distribution is heavily weighted to stars less massive than this.
Extrapolation of this birth stellar mass function to estimate the numbers of stars born with $M>8M_\odot$ (almost none of which are still on the main sequence now) suggests there are a further $\sim 1$% of neutron stars and $\sim 0.1$% black holes, though these fractions remain to be observationally confirmed and the latter number is very uncertain even as a theoretical calculation.