Machine unlearning (MU) aims to erase data from a model as if it never saw them during training. To this extent, existing MU approaches assume complete or partial access to the training data, which can be limited over time due to privacy regulations. However, no setting or benchmark exists to probe the effectiveness of MU methods in such scenarios, i.e. when training data is missing. To fill this gap, we propose a novel task we call One-Shot Unlearning of Personal Identities (O-UPI) that evaluates unlearning models when the training data is not accessible. Specifically, we focus on the identity unlearning case, which is relevant due to current regulations requiring data deletion after training. To cope with data absence, we expect users to provide a portraiting picture to perform unlearning. To evaluate methods in O-UPI, we benchmark the forgetting on CelebA and CelebA-HQ datasets with different unlearning set sizes. We test applicable methods on this challenging benchmark, proposing also an effective method that meta-learns to forget identities from a single image. Our findings indicate that existing approaches struggle when data availability is limited, with greater difficulty when there is dissimilarity between provided samples and data used at training time. We will release the code and benchmark upon acceptance.