If he stays he also becomes a scapegoat for the Catalan Media(they scapegoated Suarez when he was refusing to leave FDJ is a nobody)and fans if his presence and salary prevents additional signings and player registrations.
Barca fans booed Dembele with rumors about him wanting a pay rise some months ago. FDJ refusing to take a pay cut when everyone else is won't go down well with anyone within Barca. Staying on the same wages might possibly be the worst option for him
The narrative about pay cuts is vastly exaggerated. Most of these were deferrals, not cuts. Their "legends", Pique, Alba and Busquets, all earn a fortune. At least so far they havn't given up all that much. Barca already did run a smear campaign against Dembele. He didn't give a feck and it had zero consequences. Barca are even trying to extend his contract now, but just like with FdJ, he holds all the power. Frenke is in an even stronger position, because he is on a long-term deal. The money that is at stake here is pretty substantial even for top level footballers. He is not giving up millions of € because a few papers write mean things for a few weeks.
FdJ has all the power to decide about his future. If he wants to leave, Barca and United will find an agreement and if he doesn't want to leave, he is going to stay; probably with some kind of symbolic renegotiation so everyone can save face.
When you want to buy top players, the most important thing is to convince the player. The rest follows. Sometimes, like in the case of Sancho, this might even take a year, but once a player is committed to join another club, its usually going to happen. Barca still would like Frenkie to leave, but its not their decision.