Collaborative perception enhances the reliability and spatial coverage of autonomous vehicles by sharing complementary information across vehicles, offering a promising solution to long-tail scenarios that challenge single-vehicle perception. However, the bandwidth constraints of vehicular networks make transmitting the entire feature map impractical. Recent methods, therefore, adopt a foreground-centric paradigm, transmitting only predicted foreground-region features while discarding the background, which encodes essential context. We propose FadeLead, a foreground-centric framework that overcomes this limitation by learning to encapsulate background context into compact foreground features during training. At the core of our design is a curricular learning strategy that leverages background cues early on but progressively prunes them away, forcing the model to internalize context into foreground representations without transmitting background itself. Extensive experiments on both simulated and real-world benchmarks show that FadeLead outperforms prior methods under different bandwidth settings, underscoring the effectiveness of context-enriched foreground sharing.