I was a dedicated paleo eater for nearly three years before losing weight -- at 5' 4.5" I was never over 125 lbs, usually around 120. I'll turn 43 in April and have "carried" that weight for most of my life, never fluctuating more than four or five pounds.
This is difficult for me to admit and I'm sure I'm opening myself to criticism and downvoting and whatnot, but I am currently eating disordered. I decided last year that I wanted to lose ten pounds, started restricting calories and doing daily intermittent fasting and lost the first ten. It wasn't enough, so I've just finished losing another ten.
Oddly, at 99 pounds I don't feel (physically) unhealthy. I walk my dog about 4.5 miles every day, rain or shine, and keep a careful watch on my energy levels. The only impact I've noticed on my health was the expected amenorrhea.
Anyway, to answer your question, yeah. If someone wants to lose the fat there's nothing inherently "permanent" about it. In my experience the amount of caloric intake matters just as much as the types of caloric intake. Quantity and quality.