Interesting plant! It seems obvious a succulent.
As far as I can see the flower, I suppose the plant belongs to the family Gentianaceae.
I am tempted to say it's Sabatia arenicola. A form with white flower which has developed a succulent appearance, more like I seen in pictures on the internet.
Plants that grow in the coastal marine sand frequently develop succulent habit, similar to the desert plants, because they have to face the same requirements to save fresh water.
