Suppose a normal galaxy like ours.

Heavy stars are produced by the galaxy, converting cold gas into black
holes or heavy neutron stars.

Supernova explosions aren't symmetric, most stars receive a "kick" when
transforming into a black hole or a neutron star.

The resulting vector (that I would assume has random components), has
sometimes a component in the direction of the doomed star's orbit, or a
direction against its orbit.

If it is in the direction of its orbit around the galaxy center, the
star has a constant velocity away from the center, it will move away
from the center until the galaxy's gravitational tug retains it.

If its in the direction against its orbit, the star will spiral into the
center of the galaxy.

As eons pass, the dead stars accumulate either at the center of the
galaxy or in a diffuse halo of invisible matter around the galaxy.

This invisible mass can't explain the sorely needed black matter?

Recently, a population of black holes has been detected at the center of
our galaxy.

Columbia University. "Tens of thousands of black holes may exist in
Milky Way's center." ScienceDaily. ScienceDaily, 4 April 2018.
www.sciencedaily.com/releases/2018/04/180404133532.htm.

Couldn't a symmetrical population of dead and invisible halo stars make
for the modified gravity we see?

As more and more gas is processed into dead stars (a fast process, since
huge stars live a short life) these populations grow and grow, without
any limit.

Trees are always growing. Dead cells make for their rigidity...

[[Mod. note -- These black holes are more massive than most stars,
so dynamical friction (
https://en.wikipedia.org/wiki/Dynami...uitive_account
) causes them to gradually sink towards the center of the galaxy.
This means that there may be a high density of black holes near the
center of the galaxy. But, because these black holes are concentrated
at the center of the galactic, they can't explain flat galaxy rotation
curves. To explain those (without MOND) dark matter must be widely
distributed throughout the galaxy.
-- jt]]