Fluid antenna (FA) has become a highly promising technology and has recently been used to enhance the integrated sensing and communication (ISAC) system. However, the scenario where sensing targets act as eavesdroppers in ISAC and how to maximize the sum secrecy rate has not been addressed. This letter investigates secure transmission in FA-aided ISAC systems, where the spatial agility of FAs enables enhanced physical layer security. We jointly optimize antenna position vector (APV) and beamforming to maximize the multiuser sum secrecy rate, which complicates the solution process. To solve the resulting non-convex problem, we use a block successive upper-bound minimization (BSUM) algorithm, which incorporates the proximal distance algorithm (PDA) for closed-form beamformer updates and extrapolated projected gradient (EPG) for APV optimization. Simulation results show that the proposed FA-ISAC scheme achieves over 20$\%$ sum secrecy rate gain compared to fixed-position antenna (FPA) systems.