DISCLAIMER: We may have acted as if the following is 100% real, but it is in fact a joke. Spain's really good at their version of April Fool's Day.
Here would be one way to overcome the ignominy of fielding an ineligible player: poach your crosstown rival's top office coordinator. Reportedly, that is what Real Madrid would have done in light of the gaffe that led to their dismissal from the Copa del Rey. But alas, it was an "inocentada."
According to AS, the joke goes that Real Madrid president Florentino Pérez has acquired Jacinta Llorente from Atlético Madrid. You may not know her, but every time Atlético file transfer paperwork or release an XI or have you saying "hey, this club seems really well-run and above-board, unlike those folks across town," she is responsible. (That part is true. Now for some lies.) Llorente will depart for Real next season after many years at the Calderón as Pérez seeks organizational restructuring in light of the Denis Cheryshev ineligibilty fiasco and the failed David de Gea transfer from August.
(Ah, the irony of having an obscene sponsorship deal with Microsoft and struggling to take care of the little things.)
However, it appears her appointment as Real's chief organizer did not come easily. Per the jokesters over at AS, Pérez phoned Miguel Ángel Gil and inquired about Llorente's availability. Gil went to Diego Simeone, who said as long as Pérez promised not to bid for Antoine Griezmann, he would sanction Llorente's departure. Pérez agreed, and Llorente will move despite rejecting Real's offer of VIP tickets and a Fly Emirates world tour.
It was at this point that the story got interesting, as Real have never been reputably linked with Griezmann and Atlético would shut Pérez down if he were to make an approach anyway. Regardless, Atleti will be loath to lose an important organizational figure, and now we have to hope the club doesn't spiral by not tracking its loaned players and such.
(I think they'll be okay.)