This work studies near-field secure communications through transmit beamfocusing. We examine the benefit of having a protected eavesdropper-free zone around the legitimate receiver, and we determine the worst-case secrecy performance against a potential eavesdropper located anywhere outside the protected zone. A max-min optimization problem is formulated for the beamfocusing design with and without artificial noise transmission. Despite the NP-hardness of the problem, we develop a synchronous gradient descent-ascent framework that approximates the global maximin solution. A low-complexity solution is also derived that delivers excellent performance over a wide range of operating conditions. We further extend this study to a scenario where it is not possible to physically enforce a protected zone. To this end, we consider secure communications through the creation of a virtual protected zone using a full-duplex legitimate receiver. Numerical results demonstrate that exploiting either the physical or virtual receiver-centered protected zone with appropriately designed beamfocusing is an effective strategy for achieving secure near-field communications.