A maximum stellar surface density $��_{max} \sim 3 \times 10^5\,{\rm M_\odot\,pc^{-2}}$ is observed across all classes of dense stellar systems (e.g. star clusters, galactic nuclei, etc.), spanning $\sim 8$ orders of magnitude in mass. It has been proposed that this characteristic scale is set by some dynamical feedback mechanism preventing collapse beyond a certain surface density. However, simple analytic models and detailed simulations of star formation moderated by feedback from massive stars argue that feedback becomes {\it less} efficient at higher surface densities (with the star formation efficiency increasing as $\sim ��/��_{crit}$). We therefore propose an alternative model wherein stellar feedback becomes ineffective at moderating star formation above some $��_{crit}$, so the supply of star-forming gas is rapidly converted to stars before the system can contract to higher surface density. We show that such a model -- with $��_{crit}$ taken directly from the theory -- naturally predicts the observed $��_{max}$. $��_{max}\sim 100��_{crit}$ because the gas consumption time is longer than the global freefall time even when feedback is ineffective. Moreover the predicted $��_{max}$ is robust to spatial scale and metallicity, and is preserved even if multiple episodes of star formation/gas inflow occur. In this context, the observed $��_{max}$ directly tells us where feedback fails.

5 pages, 5 figures. Submitted to MNRAS. Comments welcome!