The high cost of model training makes it increasingly desirable to develop techniques for unlearning. These techniques seek to remove the influence of a training example without having to retrain the model from scratch. Intuitively, once a model has unlearned, an adversary that interacts with the model should no longer be able to tell whether the unlearned example was included in the model's training set or not. In the privacy literature, this is known as membership inference. In this work, we discuss adaptations of Membership Inference Attacks (MIAs) to the setting of unlearning (leading to their "U-MIA" counterparts). We propose a categorization of existing U-MIAs into "population U-MIAs", where the same attacker is instantiated for all examples, and "per-example U-MIAs", where a dedicated attacker is instantiated for each example. We show that the latter category, wherein the attacker tailors its membership prediction to each example under attack, is significantly stronger. Indeed, our results show that the commonly used U-MIAs in the unlearning literature overestimate the privacy protection afforded by existing unlearning techniques on both vision and language models. Our investigation reveals a large variance in the vulnerability of different examples to per-example U-MIAs. In fact, several unlearning algorithms lead to a reduced vulnerability for some, but not all, examples that we wish to unlearn, at the expense of increasing it for other examples. Notably, we find that the privacy protection for the remaining training examples may worsen as a consequence of unlearning. We also discuss the fundamental difficulty of equally protecting all examples using existing unlearning schemes, due to the different rates at which examples are unlearned. We demonstrate that naive attempts at tailoring unlearning stopping criteria to different examples fail to alleviate these issues.