In a recent Kurzgesagt video about black dwarfs, it mentions that over extremely long periods of time, it may be possible for black dwarfs to slowly transform (from degenerate matter I'd assume) into iron through quantum tunneling, but it does not go into any further depth. Through what process/mechanism would this happen? Would a lucky quantum fluctuations give an atom enough energy to engage in fusion? That would require quite a bit of energy, thus being extremely uncommon. Sorry, I'm a novice when it comes to quantum physics.
I guess this is talking about a form of pyconuclear reactions. (I can't find a good, free reference, but googling on the name brings up plenty of sources).
In cold, degenerate matter, such as in a white dwarf, the non-degenerate matter can freeze into a crystalline lattice. As the white dwarf continues to cool, then after 10-20 billion years or so, the heat capacity falls as per the Einstein-Debye model, and the temperature drops rapidly.
However, even at zero temperature, the ions in the lattice have zeropoint vibrations (think of the ground state of a harmonic oscillator). As such, there is a non-zero probability of being able to tunnel through the coulomb barrier and fuse with another ion.