Ah, that is clearer. That is a prolapse, either of the intestines or the ovary duct (not sure of the structural details, ovipositor?).
Has the fish been cleaning a site on the tank bottom in preparation for laying eggs? Since this fish is larger, I presume its the female? I've seen very small tubes extend when clowns lays eggs, but not this pronounced, or for this long. You might try posting one of the pictures over on the clownfish forum to see if they consider this normal or not.
If it is a prolapsed intestine, there isn't any real treatment. The fish sometimes retract them and other times they get infected.
Jay