Bizarre star could host a neutron star in its core

[Jackalope]

The combined mass of the neutron star at the center and red giant around it is almost certainly greater than the minimum mass needed to overcome neutron pressure and force the object to further collapse into a black hole.

The question is when would this collapse happen?

You're probably correct on that. The fly in the ointment is these objects "form" presumably after the host star has already progressed into the red giant phase. The mass is there, but not the density, which as I understand it is the important metric. It's an odd problem as stars with sufficient mass to become black holes (or even neutron stars) are not thought to go through the red giant phase.