When would you store a summary of a document in the vector DB but retrieve the full text for the LLM?

How do you implement "Long-Term Memory" for an agent so it remembers a user's preference from a conversation that happened three weeks ago?

What is Hypothetical Document Embeddings (HyDE)? How does asking the LLM to "write a fake answer first" improve the search results?

In a production system where agents operate over long time horizons (minutes to hours), how would you manage state persistence and recovery?