Can a Christian become demonized?

This question has divided millions of Christians. The Bible doesn't give us a clear answer. The arguments for/against are either anecdotal or theological.

What does Church History reveal? 

One of the earliest theologians in Church History, Tertullian (AD155-AD220), in fact, the man who gave us the word "Trinity," gave us his answer when he wrote:

"The Lord Himself is witness that we have the case of the woman who went to the theater and came back possessed. Accordingly, in the exorcism, when the unclean creature was rebuked for having dared to attack a believer, he firmly replied, “And in truth I did it most lawfully, for I found her in my domain.”  Tertullian (c. AD197, W), 3.90.

I find it interesting that the word he used is translated into English as "possessed." Today, it is common to use the word "demonized" instead of the word possessed. Tertullian was not writing in Greek, but rather Latin, and I am really not sure if there is a similar distinction in Latin as there is in Greek.

For those whose mind is made up that Christians cannot become demonized/possessed, Tertullian's testimony probably won't matter. If you are convinced Christians can/do become demonized/possessed, then you will find support for your position in the testimony from the end of the 2nd Century.