Open Circuit (Parallel):

A parallel circuit has more than one path for current to flow.  Current will continue to flow as long as a complete path is given through one or more of the remaining paths if one of the paths is opened.  It does not mean which you cannot stop current flow by a parallel circuit through opening it at one point; it means which the behavior of a parallel circuit depends on where the opening occurs.

Figure: Open Parallel Circuit - Total

In that condition where a parallel circuit is opened at a point where just branch current flows, then only that branch is open and current continues to flow in the rest of the circuit that was display in the Figure.

Figure: Open Parallel Circuit - Branch