Some of the hydrogen in the world around us is deuterium, again mostly from the big bang. When your body was assembled, and when you drink water/breathe, some of the generally-hydrogen sites in our bodies happen, instead, to be deuterated.
In very rare cases most of the energy might also be carried away by the neutrino that is produced as well, so decay to hydrogen is not impossible in a vacuum.
Hence, there is far too much energy released for the electron to stay bound in essentially any case. If the neutrino carries away all the energy (with momentum conservation soaked up mostly by the recoiling proton), it could re-bind, but that process should be exceedingly rare. In that case, the result would see an (excited, probably) hydrogen atom recoiling away from the invisible neutrino.
For example: https://en.wikipedia.org/wiki/Beta_decay
A great place for a reader to begin to reach their own conclusions is here: https://en.wikipedia.org/wiki/Neutron%E2%80%93proton_ratio
Thank you for the correction.