CX Cloud from Genesys and Salesforce - Timing Out an Inbound Message interaction

The problem is that on Salesforce side we can get a phone calls and they do time-out after few seconds and get back to the queue, so any other agent can pick it up, can that happen also with the Web Messaging inbound messages? For now as far as we see inbound messages do get assigned to one agent on Salesforce side and stick to it without moving it back to the queue for other agents if specific agent is staying available,but is inactive.