Introduction: Bereavement support is an integral element of palliative care. Emerging evidence stipulates that bereavement support should be reserved for those most at risk of poor outcomes. While this evidence makes identifying those at risk of experiencing a complex bereavement a necessary first step, it has been difficult to arrive at a consensus as to whom that should be. Aim: To explore whether palliative care in-patients with advanced disease are concerned about the bereavement needs of others and, if so, is it their next-of-kin. Design: A qualitative study using semi-structured interviews, and thematic analysis using a constant comparative method. Setting/participants: Patients identified by their physicians as being aware of their limited prognosis (n = 19) in a specialist palliative care service in Sydney, Australia. Findings: Three key themes emerged: 1) Families considered close and supportive may not require bereavement follow-up; 2) Families with previous significant losses or who have more complex lives are perceived by patients as having greater risk; and 3) Asking palliative care patients about whom they are most concerned in their network after their death is difficult but possible. Conclusions: There are potentially people in the palliative patients’ networks who may be in need of bereavement support, but who are unlikely to be informed about available bereavement services. New strategies are needed to identify people who may benefit from bereavement support.