There's a sign on Northern ticket machines, such as the ones at Worksop, that says tickets should be bought on the train at the first opportunity if the ticket machine cannot be used, as in this case, and the ticket office is closed (or there's no ticket office).
However, boarding the train without a ticket and asking to buy a ticket onboard is still likely to result in an allegation of an offence by Northern, or a demand to pay a Penalty Fare.
As such, I think that a reasonable person would, knowing the above to be true, find another means of transport rather than using the train.
Of course, the OP has the option of going to the station anyway, taking a picture of the sign precisely as it appears at the time they're travelling, and arguing their case if they're accused of trying to avoid paying.
For reference, the most recent time I used a Northern ticket machine, the wording in place was: "Everyone must have a valid ticket before boarding a train. If this ticket machine is not working, or you are having problems in obtaining your ticket, please visit the ticket office. If the ticket office is closed, or if this is a station without a ticket office, please board the train and pay at your earliest opportunity." To me this read as unclear because the first and last sentences actually contradict one another. In my view, it's likely that the customer is entitled to rely on the last sentence without the first one contradicting its meaning, though, because otherwise the notice is rendered nugatory.
But you can simply buy a flexible ticket of the sort that you want from any website now. It's very much a niche market to want to buy a ticket to travel from a station when there are no trains running.
It's certainly something which will arise infrequently. However, it will continue to arise regularly for as long as there are stations with a frequent service Monday - Saturday, and no service at all on Sundays. At the moment there are many such stations across the country, and they're likely to stay that way for the foreseeable future.
IMO all online ticket purchasing sites and TVM's that have itinerary functionality should start with two options
- itinerary mode targeted at those who do not know peak / off-peak / super-off-peak times then open return / day return so they buy the correct ticket for the journey. TVM's while prioritising an immediate or soon outward journey should allow for a later time or future day.
- ticket selection mode which presumes the purchaser knows the validity of the tickets they are purchasing. Without been cumbersome there should be a screen where the purchaser confirms they understand this. Better still once the ticket(s) have been selected outline the validity e.g. off-peak start times, only valid via xyz etc.
This would certainly be a good start. The first button could be labelled "I would like to see the available train times and prices" and the second one labelled "I already know which ticket I want". There would also need to be something making clear that Advance tickets are only available for sale through the former button though.