Would a dying star have a larger or smaller proportion of hydrogen, relative
to heavier elements as helium and carbon, than would main sequence stars.
Why?

Smaller proportion of hyrogen

"As a star like the Sun ages, it exhausts the hydrogen that fuels its
nuclear fusion, and increases in size to become a red giant."

http://heritage.stsci.edu/2000/25/caption.html "A Dying Star in
Globular Cluster M15" The Hubble Heritage Project

Sincerely,

Wonko

Thanks!  Excellent Answer!