We investigated the phenomenon of incomplete wetting of a high-energy liquid subphase by drops of pure amphiphilic molecules as well as drops of amphiphile solutions that are immiscible with the subphase. We show that amphiphiles escape across the contact line of the drop, move on the subphase/vapor interface, and form a submonolayer or full monolayer external to the drop. If this monolayer is sufficiently dense, then it can reduce the surface tension of the subphase, raise the contact angle of the drop, and prevent the drop from fully wetting the subphase. This phenomenon is called autophobing and has been extensively studied on solid substrates. For the liquid subphase studied here, we measure the surface tensions of the three relevant interfaces before and after the drop is deposited. The measured surface tension external to the drop shows that amphiphiles can move across the contact line and form a monolayer outside of the drop. In some cases, at equilibrium, the monolayer is in a sufficiently packed state to create the nonwetting condition. In other cases, at equilibrium the monolayer density is insufficient to lower the surface tension enough to achieve the nonwetting condition. Unlike on solid substrates where the formation of the monolayer external to the drop is kinetically hindered, the amphiphiles can move rapidly across the liquid subphase by Marangoni-driven surface transport, and local equilibrium is achieved. However, because the amphiphile inventory and subphase area are limited, the achievement of autophobing on a liquid subphase depends not only on the instrinsic subphase/amphiphile interaction but also on the total amphiphile inventory and area of the liquid subphase.