[deeths]

Here's an explanation of how these objects can remain stable I had posted previously, for folks that don't want to go through the whole other thread:

Because the density of the neutron star and the Red Giant are so different (average Red Giant density is about the same density as water), the neutron star can keep a distinct structure/orbit for 1000 years or so. When it gets to the core, fusion occurs in a halo around the neutron star instead of through the normal sort of fusion you'd get in a Red Giant core. This leads to a different ratio of nuclear isotopes, which is how you can determine these objects aren't typical Red Giants.

The resulting objects survive around 70 million years before the neutron star core absorbs enough mass to turn into a black hole. However, the predicted rate of birth/death of these objects indicates there may be a few of these in the galaxy at any given time.