I'd imagine that at that point, the expansion of the universe would nullify the tiny amounts of gravity between the particles after the supernova. The only way I'd imagine them staying together is them forming black holes, which this paper in Kurzgesagt's sources list seems to say is unlikely
The low-mass progenitors [black dwarves with iron cores] will meanwhile have compact iron cores but thin envelopes which may result in dynamics comparable to stripped-envelope CCSNe today, and with little accretion after core bounce the shock may expand almost unimpeded. Exact luminosities are difficult to determine without simulations, but the low masses may similarly reduce electromagnetic yields. Compared to CCSNe today, we might expect a similar neutrino luminosity as the iron core collapse should be comparable. Gravitational wave emission of the proto-NS may be similar, but without excitation from convection in the infalling matter one might expect less driving of the oscillation. Furthermore, the progenitor is likely highly spherical which will weaken the gravitational wave signal. For all masses considered, it seems unlikely that a black hole should form.
Of course, I don't know near enough to actually understand much of what this paper is saying, so I could be completely misinterpreting this.