If the pre-satellite days, if the station tape-delayed a show and the net did a special report, it was up to the station to handle it. That could involve anything from filling time with promos to sitting on a station ID slide for the duration of the cut-in.
If the special report ran very long, the station might fill with back-up programming and might even choose not to air the scheduled show at all. (For instance, if you’d only see the first five minutes of the show.)
Now, with satellites, stations often have a “clean feed.”