What about the deaths of the smallest stars in the universe?

We all know about the life and death processes of stars from about the
mass of the Sun on upto super-sized blue stars. The end results are
white dwarfs, neutron stars, and blackholes. But there are a class of
extremely tiny stars, the smallest red dwarfs, which I can't imagine go
through the same process as even our Sun. The reason I believe that is
because stars like the Sun are not convective down at their cores, the
main process for heat transfer at the core is through radiation, but red
dwarf stars are mainly convective, even inside their cores. As such,
these red dwarfs would be very efficient at converting most of their
store of hydrogen into helium, unlike the more massive stars which only
convert the hydrogen inside their physically distinct cores.

So these red dwarfs will last hundreds of billions and trillions of
years at the main sequence, doing exactly what they are doing right now.
So what happens when their hydrogen stars running out finally? Do they
go through the same phases as stars like the Sun do? Do they become red
giants, blow off their outer layers into planetary nebulae, with a white
dwarf in the middle? Or do they just remain at the main sequence, until
their hydrogen runs out, and they go straight into a helium white dwarf
stage without going red giant? I mean this stuff isn't expected to
happen at all in the current universe, it's not old enough yet, but has
anyone actually done a theoretical study of this?

Yousuf Khan