The bubble algae we see regularly in our tanks is Valonia ventricosa… All Valonia sp. (only 3 in the genus) are single-celled, multinucleate (each cell contains multiple nuclei) organisms and contrary to what is often said, none of them produce or contain spores.
As they are single cells (one of the largest on earth), any piece of the bubble or even the liquid in the tissue can and will produce a clone of the original. Any fish or invert eating a bubble will break the cell wall and release a cloud of trouble. The safest option is to remove the host rock from the tank and chip away the rock where the bubble is attached via its Rhizoid (root structure).