Anemone's in general can multiply by fission, but there a good number of them that do not unless a pair of scissors is taken to them and they are cut in half through the mouth.
There are only two anemones that split naturally and those are BTA's and H.Magnificas (Ritteri). Carpets like Haddoni's bud. All anemone's spawn, but not all will spawn in captivity.
Now in terms of the sebae there is a lot of debate on how it actually reporduces because no one has actually documented any natural splitting/fission of this anemone in captivity or the wild, while they have some documentation of reproduction by budding.
Now, this guy, has a bleached and dyed yellow anemone that was doing the same thing as yours now with the line going up looking like it was gonna split. His sebae died.
http://www.myfishforum.com/general-m...splitting.html
Do you or your friend by chance have a picture of this anemone. There are a couple different subsects of the sebae species, including Crispa and Malu. The Malu has more color varients including yellows and pinks, while the Crispa, to be considered healthy, is naturally a tan/brown color with purple tips and sometimes a purple or green sheen.