Undefined behaviour for room directory entries when a HS is no longer present in a room

It seems that none of the specs currently define the correct behaviour in handling room metadata (name, topic, ...) for the following situation:

1. User A on example.com homeserver adds room to example.com's public room directory
2. User A leaves room, and no example.com users remain, meaning the HS ceases to receive or process room updates
3. User B on example.com views public room directory entry for the room in question

Empirically, Dendrite apparently responds to this by retaining the metadata at the moment the user left, and not reflecting any further updates to it, but still showing the stale room metadata in the directory.

Ideally, a homeserver should continue maintaining the room metadata even after the user has left, at least until the room is removed from the directory explicitly (possibly peeking-over-federation is relevant here?). Failing that, the intended behaviour should at least be specified explicitly.

Start by reviewing the Matrix room-directory specification and the linked peeking-over-federation proposal. Compare the described Dendrite behavior with the desired handling after the last local user leaves, then specify whether metadata remains current or is removed until explicit directory removal.