Since the rapid expansion of large language models (LLMs), people have begun to rely on them for information retrieval. While traditional search engines display ranked lists of sources shaped by search engine optimization (SEO), advertising, and personalization, LLMs typically provide a synthesized response that feels singular and authoritative. While both approaches carry risks of bias and omission, LLMs may amplify the effect by collapsing multiple perspectives into one answer, reducing users ability or inclination to compare alternatives. This concentrates power over information in a few LLM vendors whose systems effectively shape what is remembered and what is overlooked. As a result, certain narratives, individuals or groups, may be disproportionately suppressed, while others are disproportionately elevated. Over time, this creates a new threat: the gradual erasure of those with limited digital presence, and the amplification of those already prominent, reshaping collective memory. To address these concerns, this paper presents a concept of the Right To Be Remembered (RTBR) which encompasses minimizing the risk of AI-driven information omission, embracing the right of fair treatment, while ensuring that the generated content would be maximally truthful.