Survival models on networks describe the time-evolving dynamics of complex systems, but existing frameworks suffer from two key limitations: First, many past approaches implicitly assume independent censoring, which can introduce substantial bias. Second, point-process-based models often emphasize only sending behavior and overlook shared latent structure between interacting nodes. Recent work has incorporated copulas into deep survival models to mitigate censoring bias, but these methods do not capture topological role structure. Another line of research combines survival analysis with the Mixed-Membership Stochastic Blockmodel (MMSB) to model heterogeneity via role-specific hazard rates; however, it typically assumes structural independence and therefore misses important correlations between roles. To bridge these gaps, we apply an improved Copula–MMSB mechanism and propose the first Survival Fully-Collapsed Copula Mixed Membership Blockmodel. Our framework jointly models time-to-event dynamics and complex dependencies among latent roles. On the Enron benchmark, it surpasses state-of-the-art survival blockmodels in both predictive likelihood and structural interpretability. Additionally, the model admits an exact closed-form discrete distribution over role pairs, which enables a fully collapsed Gibbs sampler and avoids the slow mixing and poor convergence common in non-conjugate inference. In simulations, this yields a 100× improvement in sampling efficiency over semi-collapsed baselines.