When an inbound call comes through Contact Center to a user, wether it is an external or an internal call, the caller does not receive a ringback and the callee (the user) does not receive a ring alert.
As an administrator, try toggling the Agent Script for the affected user, as follows:
1. Log into Configuration Manager for Contact Center;
2. Navigate to Users -> Phone -> Channels and Scripts linked to this Agent;
3. Under Script Name - PBX number, select Agent DID script, and Save;
4. Under Script Name - PBX number, select Agent Extension script, and Save;
Agent script possibly in corrupt state
If toggling the Agent Script does not resolve the issue, please create a case with 8x8 Technical Support.