Over the past 15 years, a growing body of research into the issues care-experienced people face when accessing higher education (HE) has led to welcome support developments to attempt to redress inequalities. However, such support ceases upon completion of undergraduate degrees. Without continued support, constraints in accessing taught postgraduate study can lead to limitations in future careers, earning potential, and future stability for care-experienced people. Until now, there have been no insights into why care-experienced people wish to study at the postgraduate level, as well as whether and how they may be constrained or enabled by their care backgrounds when doing so. Using data from a qualitative longitudinal study of care-experienced graduates' transitions out of HE, the paper illustrates how this 'undergraduate cliff edge' in support constrains the feasibility of progressing into and through taught postgraduate studies. The absence of often taken-for-granted support, such as a family home, means that entering postgraduate studies and facing this cliff edge is risky and perpetuates the sense of instability felt in childhood. The paper concludes by proposing recommendations for policy and practice to enable the creation of equitable opportunities to reduce risk for this group to comfortably study at the postgraduate level.