Yes, a broken loop may still have detection capabilities. It depends on the type.
Eutectic salt types can have a an open loop and still function
The Fenwal CFD® System maybe wired to employ a "loop" circuit. In this case, should an open circuit occur, the system will still signal fire or overheat. If multiple open circuits occur, only that section between breaks becomes inoperative.
If it is a gas-type, then no.