When a neutron star is engulfed within the envelope of its giant star companion, it spirals toward the center as drag forces from the surrounding envelope tighten its orbit. During this common envelope phase, orbital energy and momentum are deposited into the giant star’s envelope at the expense of the neutron star orbit. In some cases, this deposition of energy may be sufficient to remove the envelope and leave behind a transformed binary system of the neutron star and giant core. In other cases, the neutron star sinks to the center of its companion and merges with the core, potentially setting the stage for a giant with a neutron star core, or Thorne-Zytkow Object (TZO). This talk focuses on this stage of neutron star inspiral and coalescence, and the “initial conditions” that this phase imparts on nascent TZOs. The outcomes of this phase may hold crucial clues that determine the persistence and fate of these unusual and fascinating objects.