Radiative near-field (RNF) beamforming is vulnerable to blockages that disrupt Fresnel zones. This letter proposes an obstruction-unaware wavefront shaping strategy inspired by catastrophe optics. By superimposing a calibrated quartic phase, we generate a Pearcey-like wave packet that exhibits structural stability against perturbations. We establish a fair comparison protocol where the quartic beam is calibrated in free space to avoid exploiting obstruction knowledge. Numerical results demonstrate up to 8.5~dB SINR gain over conventional focusing for multi-user scenarios near the depth-of-focus limit. Crucially, this gain stems from improved channel conditioning under partial blockage, which mitigates the severe noise amplification inherent to zero-forcing precoding.