Some couples may choose to continue the pregnancy unable to decide for termination of pregnancy. Such situations recently occurred in neonatology units and may lead to neonatal palliative care. Faced with all uncertainties inherent to medicine and the future of the baby, medical teams must inform parents of different possible outcome step by step. Consistency in the reflection and intentionality of the care is essential among all different stakeholders within the same health team to facilitate support of parents up to a possible fatal outcome. This issue in perinatal medicine seems to be to explore how caregivers can contribute in the construction of parenthood in a context of a palliative care birth plan.