It has been proven by Tolkien himself
that Eru did permit the souls of slain Elves to be reembodied once
hurts have been healed in the Halls of Mandos. It has also been
said that some, such as Feanor, would be given a sort of punishment, to
in the Halls of Mandos.
While we know that Feanor is kept in the Halls of Mandos, what of the rest of the House of Finwe? One of the most depressing elements of the First Age is the fact that all of the House of Finwe, save Galadriel, and Finarfin, were slain. The possibility of their reembodiment is uplifting, seeing as it's a wonderful thought that perhaps this doomed family is together again in Valinor.
The only members of the House whose actions could have brought about the same fate as Feanor are Maedhros and Maglor, who stole the two silmarils from Eonwe and his host. We know Maedhros died, though all we learn of Maglor is that he roamed the beaches singing of the sorrows of the Elves.
All other members of the house of Finwe were valiant Elves, (not to say that Maedhros and Maglor weren't!) and despite their doom in the First Age, were deserving of the happiness that Valinor would bring.
One theory regarding the fate of Feanor said that when Miriel died, she eventually joined Vaire the Weaver. Perhaps Eru or the Valar, after time, allowed Feanor to join the mother who loved him so much? And perhaps Feanor finally learned to control his fiery spirit.