Mat.12:28 -29 "But if I cast out demons by the Spirit of God, surely the kingdom of God has come upon you. Or how can one enter a strong man’s house and plunder his goods, unless he first binds the strong man? And then he will plunder his house."
Luke 11:21-26 "When a strong man, fully armed, guards his own palace, his goods are in peace. But when a stronger than he comes upon him and overcomes him, he takes from him all his armor in which he trusted, and divides his spoils. He who is not with Me is against Me, and he who does not gather with Me scatters. When an unclean spirit goes out of a man, he goes through dry places, seeking rest; and finding none, he says, ‘I will return to my house from which I came.’ And when he comes, he finds it swept and put in order. Then he goes and takes with him seven other spirits more wicked than himself, and they enter and dwell there; and the last state of that man is worse than the first."
These, as you've probably guessed, are the scriptures detailing possessions. It indicates that when a demon is cast out (strong man overpowered) he can repossess if the house is "empty." However, if one becomes a Christian he is "filled with the Holy Spirit" and has "Christ in [him]." So, Jesus has power to cast out demons from unbelievers but if the unbeliever does not become a believer he will remain under the power of darkness