It does not say you have to keep an active subscription for continued operation. The page only says:

  Claim your Muse Home Link
  Free with an active Muse subscription

https://muse.ai/deviceterms "If your Muse subscription terminates or expires, your Muse Device will cease to function as described in these Device Terms and the device documentation. The device's capabilities will be unavailable until an active subscription is restored."

https://gadgets.muse.ai/home-link "Muse Home Link itself only runs official firmware and can’t be reflashed"