Special stops are very much the norm at some operators and less so at others. I have participated in many but there do seem to be reports around the country that other places are somewhat lacking. On my patch a number of “last trains” are semi-fast - and do run at fairly high linespeeds between stops - but can get converted into stoppers if people need to get home. For example, when the 0102 Victoria-Brighton was a more regular fixture in the timetable, it often used to get the all-stations calls from the 0042 Victoria-East Croydon if that was cancelled - and Coulsdon South and Merstham if the 0014 to Three Bridges went wrong. Likewise the limited-stops 2304 London Bridge-Uckfield makes calls at Hever/Cowden/Ashurst if there’s been disruption and people have missed connections into the 2204, which is the last stopping service. Much the same applies across GTR and indeed around the South as a whole. SWT once pulled a particularly impressive additional call at somewhere like Brookwood (IIRC), late at night, as someone got stranded there, who sent them a slightly desperate tweet with only a few minutes until a train passed through - and it stopped...
Wasn't it recently said that the crew would have to have start/stop route knowledge for all stations along their route, whether they were expected to stop there or not?
Correct. Crews of passenger services need to be able to understand the protocol to safely stop at any station en-route... unless a particular type of stock/service can’t call in passenger service at a specific station, in which case you would only be familiar with its location for evacuation and also if there was a platform starter signal to be stopped at / speed restriction / other infrastructure feature.
I sign a number of routes where I have never had to call at the smaller stations since I learnt them, years ago - but I can be asked to demonstrate or use my knowledge of station names and locations, access arrangements at all hours, platform lengths, signals, off indicators and repeaters, dispatch positions, interchanges, the points at which to make announcements on approach, etc.