Large Language Models (LLMs) are increasingly used to ``professionalize'' workplace communication, often at the cost of linguistic identity. We introduce "Cultural Ghosting", the systematic erasure of linguistic markers unique to non-native English varieties during text processing. Through analysis of 22,350 LLM outputs generated from 1,490 culturally marked texts (Indian, Singaporean,& Nigerian English) processed by five models under three prompt conditions, we quantify this phenomenon using two novel metrics: Identity Erasure Rate (IER) & Semantic Preservation Score (SPS). Across all prompts, we find an overall IER of 10.26%, with model-level variation from 3.5% to 20.5% (5.9x range). Crucially, we identify a Semantic Preservation Paradox: models maintain high semantic similarity (mean SPS = 0.748) while systematically erasing cultural markers. Pragmatic markers (politeness conventions) are 1.9x more vulnerable than lexical markers (71.5% vs. 37.1% erasure). Our experiments demonstrate that explicit cultural-preservation prompts reduce erasure by 29% without sacrificing semantic quality.