Camera redirection aims to replay a dynamic scene from a single monocular video under a user-specified camera trajectory. However, large-angle redirection is inherently ill-posed: a monocular video captures only a narrow spatio-temporal view of a dynamic 3D scene, providing severely limited observations of the underlying 4D world. The key challenge is therefore to recover a complete and coherent representation from this limited input, with consistent geometry and motion. While recent diffusion-based methods achieve impressive visual generation quality, they often break down under large-angle viewpoint changes far from the original trajectory, where missing visual grounding leads to severe geometric ambiguity and temporal inconsistency. We present FreeOrbit4D, an effective training-free framework that tackles this ambiguity by recovering a foreground-complete 4D proxy as structural grounding for video generation. We obtain this proxy by decoupling foreground and background reconstructions: we unproject the monocular video into a static background and partial foreground point clouds in a unified global space, then use an object-centric multi-view diffusion model to synthesize multi-view images and reconstruct complete foreground point clouds in canonical object space. By aligning the canonical foreground point cloud to the global scene space via dense pixel-synchronized 3D-3D correspondences and projecting the foreground-complete 4D proxy onto target camera viewpoints, we provide geometric scaffolds that guide a conditional video diffusion model. Extensive experiments show that FreeOrbit4D produces more faithful and temporally coherent redirected videos under challenging large-angle trajectories, and our proxy further enables applications such as edit propagation and 4D data generation. Project page: https://freeorbit4d.vision.ischool.illinois.edu/