LLM API calls are becoming a ubiquitous program construct, yet they create a boundary that no existing program analysis can cross: runtime values enter a natural-language prompt, undergo opaque processing inside the LLM, and re-emerge as code, SQL, JSON, or text that the program consumes. Every analysis that tracks data across function boundaries, including taint analysis, program slicing, dependency analysis, and change-impact analysis, relies on dataflow summaries of callee behavior. LLM calls have no such summaries, breaking all of these analyses at what we call the NL/PL boundary. We present the first information flow method to bridge this boundary. Grounded in quantitative information flow theory, our taxonomy defines 24 labels along two orthogonal dimensions: information preservation level (from lexically preserved to fully blocked) and output modality (natural language, structured format, executable artifact). We label 9,083 placeholder-output pairs from 4,154 real-world Python files and validate reliability with Cohen's $κ= 0.82$ and near-complete coverage (0.01\% unclassifiable). We demonstrate the taxonomy's utility on two downstream applications: (1)~a two-stage taint propagation pipeline combining taxonomy-based filtering with LLM verification achieves $F_1 = 0.923$ on 353 expert-annotated pairs, with cross-language validation on six real-world OpenClaw prompt injection cases further confirming effectiveness; (2)~taxonomy-informed backward slicing reduces slice size by a mean of 15\% in files containing non-propagating placeholders. Per-label analysis reveals that four blocked labels account for nearly all non-propagating cases, providing actionable filtering criteria for tool builders.