Do vector databases persist past the end of the chat session?

Summary:

Want to know if vector databases can persist across chats and agents. For example, if one agent writes data to an indexed vector database during session A, will a different agent, or the same agent at a different time during session B, C, or D, be able to access the information written during session A?

Content (please ensure you mask any confidential information):

Version (include the version you are using, if applicable):

Code Snippet (add any code snippets that support your topic, if applicable):