This verse has been misapplied very badly. Other people understand it by instinct.
I will underline the key word in this passage that implies the course of action:
Matthew 12:44 Then he says, 'I will return into my house from which I came out,' and when he has come back, he finds it empty, swept, and put in order.
12:45 Then he goes, and takes with himself seven other spirits more evil than he is, and they enter in and dwell there. The last state of that man becomes worse than the first. Even so will it be also to this evil generation."
So a spirit was successfully removed. What's the problem? The house is EMPTY--nature abhors a vacuum! This is a secular axiom but its meanings are accurate.
Case in point: Alcoholics Anonymous. I've never been to one of their meetings, but what I hear tells me that they understand this passage very well: you cannot rip alcoholism (a spirit--not the name of the spirit itself but the trait it carries) without putting something in its place. This is the real way all idolatry is opposed, this is how we cure addictions: every time a wrongful thought or habit is removed, a right one must be put in its place, or a worse one will inevitably take its place (and as this verse shows, sometimes even the original one may come back as it is just difficult to sustain a vacuum without the outside force trying to pressure a person). The other place this passage is found, Jesus said "that is how it will be with this cursed generation." You can observe this from the places he preached: many were healed, and yet many of them were unrepentant, and it will be more bearable for Sodom than they.
Another practical example, and this is huge: parenting. Oftentimes parents are in the habit of ripping their children's hobbies and interests away when they feel there is fault--that is not the problem, but time after time it is observable that parents who do this with their children and fail to put something in the place (filling the same hole that the interest was trying to fill) find themselves with children who rebel the whole way and more.
At any rate, this is a key principle of deliverance and it does not escape common sense: take the bad thing out, put a good thing in. Being surgical, to make sure that whatever is put in its place does the same GOOD job without the faults.
I am reminding myself of this lately just to make sure that when I oppose ideology, I am in the habit of putting the right one in its place. None of this is (rightly) beyond common sense, but I offer this as a way to put that scripture to use and ESPECIALLY to avoid the wrongful ways it has been used by deliverance ministries. The phrase they use is "legal ground" and their theology is that of the Accuser, who wants to convince the saints that he has the "legal right" to mess with a Christian. The fact is that proper belief will protect the believer, but the only action to be taken when a spirit is accosting (even Jesus was accosted) is to fight it tooth and nail and minister healing (the infilling of the Holy Spirit) if it penetrated the person. Clearly that is what Jesus did. THEN the room is put in order, and when it is seen "empty" it must be filled.
That was a hint of solid food in that last part, but there are some that I would warn against listening to (wrongful interpretations) so I see the need to point out the flaw as a warning and the right alternative. This generally sums up the introduction of Christ also.