That band actually started as a Sabbath cover band, but pretty quickly started writing original material and abandoned the cover band idea.
Black Sabbath has actually had a lot of members die over the years, but none of the original line-up. But they actually broke up anyway, last year. Ozzy wants to concentrate on his solo band now, and Tony Iommi I think doesn't want to do the Sabbath-without-Ozzy thing anymore. Hence why they went under the name Heaven and Hell when Dio rejoined the group in 2006 or so.