I think at an ATC unit where no take-off clerance is given (due to expired CTOT) the captain taking off without one means the ensuing paperwork will not focus on the bust CTOT...
In the event that unforeseen circumstances during taxi cause a flight to miss its CTOT before being ready for departure , how is that flight normally treated? ( at least here in Europe ? )
Do you allow the flight to depart assuming it is expected to be ready for departure very soon after the exparation?
do you allow the pilot the remain at some holding point to file a delay message ? ( btw will it be treated favorably if it is know that it’s taxing ?)
Is the flight forced to return to a parking position ?
To answer the original question.
Depends on circumstance, the first step is often to put the question to the FMP (who in turn will negotiate with the NM) to see if there is any chance of moving it by a few minuts. If it's not a complicated situation they can often extend it or generate a new slot within short notice. This depends on the circumstance, if there is only one regulation involved with fairly low delays (and the network as a whole runs smoothly) they seem to be pretty good at working some magic. If the flight is subject to several regulations or delays are very high then quite often there is nothing they can do manually, at least not straight away.
The flight can not depart outside of the CTOT, so it will not just be ignored like it may have been in "the old days".
If there is scope for it (depends a bit on runway configuration and airfield circumstances) the flight tends to remain at the runway. This also makes it easier to improve the CTOT as we can tell the computer that the taxi time is very short. If it returns to stand then the taxi time is obviously much longer. Saying this I have seen aircraft having to return due to fuel issues, after pushing to expect to make a slot (which they were) and a combination of CTOT moving forward and a technical issue meant they just missed it. In this case the CTOT is less of a concern as the flight has to return to refuel, the flight plan is then suspended and once a new EOBT submitted a new CTOT generated, in that circumstance it practically turns into a normal departing flight of stand.
There is no advantage to send a delay during taxi. In fact the later you send it the worse you risk the CTOT getting, normally the least delay is incurred by filing the delay as early as possible. But the computer doesn't know if the aircraft is under taxi or on a stand when the delay is filed so it will assume the "standard" scenario of aircraft on a stand. For ready messages though the taxi time is adjusted by ATC to make sure it's as realistic as possible as a shorter taxi time increase the chances of the CTOT improving.
Now all of this is based on a non-CDM airport, so what would happen at an airport running CDM I don't know, but hopefully someone else can explain that scenario.