Single-image human mesh recovery provides a compact 3D, person-centric representation that supports analysis, animation, AR and VR, rehabilitation, and human-computer interaction. However, prevailing systems impose an intact-limb prior and degrade on people with limb loss, because fixed-topology models cannot represent residual limbs. In this work, we present ResiHMR, a residual-limb aware framework for single-image 3D human modeling. ResiHMR adopts residual-limb keypoints and introduces two components: (i) a topology-adaptive Residual Anchor-Factor Optimization module that constrains estimation to the observed kinematic subgraph of anatomically valid structures, and (ii) a geometry-based Residual-Limb Reconstruction module that estimates residual-limb boundaries and convex limb-termination geometry. These components introduce topology-aware optimization and explicit termination geometry as tools for human mesh recovery under non-standard limb anatomy. Unlike joint-removal methods in a fixed topology, ResiHMR explicitly reconstructs residual-limb surfaces and aligns optimization with limb-loss topology, which better matches prosthetic biomechanics and real-world use. To the best of our knowledge, this is the first single-image HMR system that explicitly reconstructs residual-limb surfaces and performs topology-adaptive optimization for individuals with limb loss. On a curated dataset of real-world images with limb loss, ResiHMR improves reconstruction quality under both SMPLify-X and HSMR backbones, reducing intact-joint 2D MPJPE from 41.32 to 37.40 with SMPLify-X and residual-limb 2D MPJPE from 73.61 to 23.19 with HSMR.