Most connections offer a "Hold files" property. While this property is set to yes, jobs are not allowed to move through the connection. This is mostly used to temporarily hold jobs (perhaps because there is a problem with a process downstream).
The canvas displays connections on hold as a dashed line (see examples below).
Although editing in the Properties pane is disabled while a flow is active (see activating and deactivating flows), the status of the "Hold files" property can be modified at any time through the context menu of the connection.