It never got as far as proposing any particular stock, but there was a DfT proposal back in the 2008 rolling stock plan to consolidate all the 323s with one TOC - however transfers in both directions have been mentioned at various times
The actual original DfT proposal said the Northern's 323s would go to LM and Northern would get new EMUs to replace them and provide 24 additional carriages (intended for the North West routes.) The Yorkshire RUS published after this recommended an addition of around 30 vehicles to this order in order to provide additional capacity for Yorkshire and replace the 321s.
There was never a tender put out for new EMUs for Northern though so an actual type of unit was never decided on.
However, LM put in a tender for new EMUs and the DfT proposal was updated to say Northern would receive new or cascaded EMUs which suggested that the 323 cascade would be reversed.
(Incidentally the same document said the LO 150s would go to Northern and the LM 150s would be split between Northern and FGW to compliment a new DMU delivery.)
if there'd been no electrification the 319s would have needed an alternative cascade route...
The actual details of the Thameslink cascade released have been somewhat limited. I think the only reason DfT mentioned cascaded Thameslink EMUs for the newly electrified lines so far in advance is because otherwise people would have been getting excited about receiving new EMUs and then complaining later on when they are actually told they are getting old Thameslink trains.
We shouldn't forget that other operators like NXEA have been promised a 3 figure number of extra EMUs when we're looking at how many units are left over after being released by Thameslink so I wouldn't be surprised if all the 317s and 321s released by the Thameslink program go to NXEA.