Barriers usually 'remember' what tickets have been put through. If you try and put a ticket previously used in that barrier it is usually rejected. Presumably there is a limited amount of data that can be stored in the magnetic strip given that the technology is so old. Therefore (I'm guessing) that all ticket numbers used in that barrier are stored somewhere.
I don't think the barriers are quite that sophisticated! I believe the barrier modifies the data on the strip so the ticket knows it has been through that barrier already, rather than the barrier knowing. Therefore, the next time the ticket is inserted, the ticket flags the barrier rather than the other way around.
There is a reason I suspect it is this way around. Once I had two 7-day Travelcards for successive periods as part of a course I was on in London. (What was more amazing is this was AFTER 7-day tickets had all been transfered to Oyster and these were TfL paper tickets). One evening in the first week, I mistakenly put the wrong ticket (that for the second week) into the barrier, which obviously wouldn't work.
The ticket then proceeded to fail completely, opening no barrier at all, even after the start date had passed. In the end, I had great difficulty getting it replaced to a usable ticket as 7 day Travelcards were all on Oyster now, until some very kind lady at Charing Cross managed to do it, bypassing the system somehow!
Admittedly, this is what LU barriers do, but I suspect NR ones operate in the same manner.
Seasons are likely to have the photocard number on the magnetic strip, I would imagine. This may allow a season ticket to be traced back to the holder, or at least to the ticket office where it was purchased, if it's eaten up by a machine. (I'm just guessing, but it would be an easy way to find such a ticket).
I suspect the same, now photocard numbers can be inputted so they are printed on the ticket. This way if, through excessive usage say, the print wears down on the top of the ticket, it is possible (although it is quite unreliable) to put a TIS into a mode and swipe the ticket to obtain the data from it, in a readable form.
On a different note, station usage figures are not calculated by using barrier data. Obviously, stations that do not have barriers would not work. In order to make the system uniform, LENNON (the software used for ticket analysis) uses ticket issues to calculate station entries (the origins on tickets) and exits (the destinations on tickets). Seasons and rovers are slightly more complicated - I suspect there is a 'usage' factor for seasons, and rovers are ignored completely.