What attackers do. Attackers send stolen data out through the same command and control channel they already use to control compromised systems, so no new connection is needed. This serves the Exfiltration tactic.
How to defend. Limit and monitor outbound traffic, send it through proxies and apply data loss prevention where practical. Detecting and cutting the command and control channel early prevents this as well. Set baselines for normal outbound data volumes per host.
Signs to look for. Look for hosts sending much more data out than they receive, beacon traffic that suddenly grows, and large uploads to rare destinations. A common gap is watching only for exfiltration to well-known file sharing sites while ignoring volume changes on existing channels.