A system framework is proposed and analyzed for generating polarization-resolved wideband unpredictability-enhanced chaotic signals based on a slave vertical-cavity surface-emitting laser (S-VCSEL) driven by an injected optical chaos signal from a master VCSEL (M-VCSEL) under optical feedback. After calculating the time series outputs from the M-VCSEL under optical feedback and the S-VCSEL under chaotic optical injection by using the spin-flip model (SFM), the unpredictability degree (UD) is evaluated by permutation entropy (PE), and the bandwidth of the polarization-resolved outputs from the M-VCSEL and S-VCSEL are numerically investigated. The results show that, under suitable parameters, both the bandwidth and UD of two polarization components (PCs) outputs from the S-VCSEL can be enhanced significantly compared with that of the driving chaotic signals output from the M-VCSEL. By simulating the influences of the feedback and injection parameters on the bandwidth and UD of the polarization-resolved outputs from S-VCSEL, related operating parameters can be optimized.