Timothy asked: How could a genuine believer ever become an unbeliever?
Some people who profess to be unbelievers actually just have "issues" with God. Years ago, my own step-daughter told me she didn't believe in God anymore, due to several issues she had with Him. Her complaints usually started with, "How could He..." or "If there were a God, why would He let..."
We had some very lively discussions about it. One day, she actually ran out of our house when I told her that God still loved her, even in her unbelief. My husband chased after her, then later forbade me to talk "religion" with her ever again.
He didn't forbid me to talk to her, though, and my normal speech is peppered with references to my faith. It was almost comical, if it weren't so tragic, to witness her trying to scrub her speech of any references to spiritually or religion when she and I were in a conversation. She would make a reference to prayer, then stop in mid-sentence and change "pray" to "hope". I always thought of her as a fence-sitting agnostic because of how hard she tried to make me believe that she was an atheist...
My husband died close to 5 years ago. She walked out of my life on the day of his funeral. She emailed me to say she couldn't see me anymore because, and I quote, "You remind me of death." How's that for a kick in the stomach? A couple of years ago, she showed up unannounced, drunk and stricken...so much so that I didn't recognize her at first. I welcomed her warmly. We spoke for awhile, then I drove her home.
Anyway, very recently, she called me...to apologize for the way she had treated me and to ask if she could come over on the weekend. We spoke that night on the phone for more than an hour. I was struck by how she was no longer masking any references to God. She showed up for our meeting, right on time. This is a changed woman. She's still seeking, not quite at peace, but oh, so different than she was 5 years ago.
And I said all that to give my answer to Timothy's question: I don't think they can...because He will go after His lost sheep.