Large language models (LLMs) struggle with representing and generating rare tokens despite their importance in specialized domains. We investigate whether LLMs develop internal specialization mechanisms through discrete modular architectures or distributed parameter-level differentiation. Through systematic analysis of final-layer MLP neurons across multiple model families, we discover that rare-token processing emerges via \textit{distributed specialization}: functionally coordinated but spatially distributed subnetworks that exhibit three distinct organizational principles. First, we identify a reproducible three-regime influence hierarchy comprising highly influential plateau neurons(also termed as rare-token neurons), power-law decay neurons, and minimally contributing neurons, which is absent in common-token processing. Second, plateau neurons demonstrate coordinated activation patterns (reduced effective dimensionality) while remaining spatially distributed rather than forming discrete clusters. Third, these specialized mechanisms are universally accessible through standard attention pathways without requiring dedicated routing circuits. Training dynamics reveal that functional specialization emerges gradually through parameter differentiation, with specialized neurons developing increasingly heavy-tailed weight correlation spectra consistent with Heavy-Tailed Self-Regularization signatures. Our findings establish that LLMs process rare-tokens through distributed coordination within shared architectures rather than mixture-of-experts-style modularity. These results provide insights for interpretable model editing, computational efficiency optimization, and understanding emergent functional organization in transformer networks.