This may be what is happening. It's from
http://www.carlosreef.com/AnemoneFAQ.pdf
There is something coming out of my anemone’s mouth – what is it?
Anemones only have one opening into their digestive system – their mouth. Once they digest a meal, anything that is indigestible (fish bones, etc) will come back out of the mouth when the anemone is done eating. Additionally, anemones will sometimes “deflate” in order to flush wastes out of their system or to balance internal water chemistry. This water will flow in and out of the mouth, and sometimes contains some body slime, etc. Stringy dark brown substance coming out of the anemone’s mouth is usually a bad sign – it is most often an indication that the anemone is expelling its zooxanthellae due to stress or injury. Finally, when spawning anemones release their eggs or sperm from their mouths. In the case of females, the eggs are colored pheres about the size of poppy or small sesame seeds; in the case of males, the sperm is a lightcolored cloud that looks a lot like smoke.
