  We investigate the final fate of metal deficient (MD) H burning Red Giants
under various assumptions about the amount of mass loss. Adopting a metallicity
Z= 10^(-8), we follow the evolution of 0.8 Mo models from the Main Sequence
phase till the onset of the He flash or the final cooling as a He White Dwarf,
according to the amount of mass loss. We show that MD Red Giants require
peculiarly large H-rich envelopes to support the H-shell burning and to allow
the final ignition of He, thus favouring the occurrence of He degenerate dwarfs
either as the result of single star evolution or in MD binary systems. The
evolution of our models along the He burning phase or as cooling White Dwarf is
briefly discussed.
