Genesys Cloud allows stopping a persistent WebRTC connection through the menu in Chrome browsers or the arrow icon in the client. This disconnects the WebRTC media connection but does not affect calls in progress. The menu method involves navigating to Settings > WebRTC and selecting "Stop Persistent Connection". The arrow method involves clicking the user's phone name and selecting "Stop Persistent Connection". This functionality applies across Genesys Cloud Embeddable Framework, Genesys Cloud for Chrome, Firefox, Microsoft Teams, Salesforce, and Zendesk.