As we all know well, acceptance of our Savior does not stop Satan from pouring on the temptation.
And I have seen some people I thought were so incredible lost they could never be saved miraculously turn to Jesus when they hit bottom.
Demons cannot possess a person who is saved because that person is indwelt by the Holy Spirit and are therefore protected. Demons, as we know, tremble and flee before God and can't stand to be in His presence.
No one is beyond the salvation that Christ offers provided they choose to respond to the wooing of the Holy Spirit. There have been hard-core atheists who have chosen the freedom and forgiveness offered by Christ so there is nobody who can't be redeemed.