Short answer
HubSpot's KB: blocking an IP disables the chat widget for visitors on that address. The current conversation moves to Spam and its ticket is deleted, restorable for 90 days. Because IPs can be shared or reassigned, blocks expire after 14 days.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
Repeat offenders may need blocking again after the expiry.
3. Related
Inbox channels and chat availability.