Structural credit risk models are widely used in default prediction practice, but standard formulations do not explicitly account for external support that may prevent default. We incorporate external support into the Merton and, more importantly, the Leland--Toft (LT) model with endogenous default. In the Merton model, support reduces realized default mechanically through a joint-default channel. In the LT model, anticipated support additionally raises debt value and affects equity holders' default decision. We derive closed-form expressions for the support-adjusted default boundary and default probability, and show that, under an economically relevant condition, stronger support lowers the endogenous default boundary, generating an additional indirect reduction in default risk. Empirically, we construct a newly assembled dataset of corporate debt defaults among Chinese A-share listed firms that combines bank loan defaults with bond default events. Using a composite measure of external support, we find that incorporating support significantly improves default prediction in both models. For the LT model, both the mechanical and endogenous channels contribute to this improvement, while the specification incorporating both channels delivers the strongest predictive performance. Our results highlight the importance of institutional support for structural credit risk modeling in China.