If you're in the REAR units when it leaves Liverpool Lime Street as a 4-car unit, then after it reverses at Sheffield - you should then be in the FRONT 2-units heading towards Nottingham..
At Nottingham, they normally detach the REAR 2-units, and the FRONT 2 carry on towards Grantham, Peterborough and Norwich
This from personal experience, as I've caught one of these back from Manchester Piccadilly to Nottingham - and despite NUMEROUS announcements on the train that only the FRONT 2-cars will continue on past Nottingham, the "scrum" for seats at Nottingham has to be seen to be believed.
People hammering the buttons on the units to be detached
People who WERE in the rear unit now having to get off - and trying "barge" their way back on.
I was replying to the question about whether if there's only two carriages they will run through.
In the case of four-cars, in the last year I think I've had every possibility - the front two carrying on, the rear two carrying on and even the whole four staying in Nottingham and a run across the station to get on to a different two car train carrying on. Likewise coming the other way, I've had two join ahead, two join behind, only two carry on through and my favourite, getting kicked off and then finding the continuing train already left from the other side of the station and you need to kick your heels for an hour.
It seems unless the normal (which is as you say) plan is to be followed, this only becomes clear in the approach to Nottingham. The staff are almost invariably apologetic and pleasant about it when things don't follow that plan, but I make sure I always listen to any announcement on the approach to Nottingham, and make sure I'm ready to get off if needed to give me the best chance of making it if a set swap happens.
The most fun happens if it skips out the reversal in Sheffield, as what happens in Nottingham is then completely random - all you can be sure of is that everyone will get disrupted somehow.