I think you may be wrong about there no one being alive to see it,the founder didn't die until 1951, he was still demonstrating and lecturing about it up till his death so I imagine there are people still around who may remember seeing it. However the practicioners wouldn't have stopped just because the club closed so it would have carried on perhaps under a different name but there's obviously enough information around for the society to start up teaching it again.
What I found the best thing about 'Batitsu' was the encouragement that women were given to participate.
I'm a member of the Bartitsu Society and am actively involved in the "revival" effort. Basically, for most practical purposes, Bartitsu did die out when the Bartitsu Club closed in 1902. There are persistent rumors that Barton-Wright continued to develop it and teach it privately into the 1920s, but those have never been confirmed. Thus, probably more by force of circumstances than by design, Bartitsu was left as a "work in progress" rather than as a complete, codified system.
Various practitioners, including former Bartitsu Club instructors and their students, did keep practicing similar cross-training methods, but none of them perpetuated the Bartitsu name. Barton-Wright himself seems to have shifted gears and threw himself into his other big passion, which was physical therapy; he persisted with that career for the rest of his long life (dying in 1951 at the age of ninety).
Also, there are a few judo and jujitsu clubs in England that can trace their origins back to former Bartitsu Club instructors Yukio Tani and Sadakazu Uyenishi. Tani taught at the famous London Budokwai for many years, and that club is still gong strong.
The modern revival of Bartitsu began in 2002, after Barton-Wright's original articles were rediscovered in the British Library archives and published online on the EJMAS website. We train in what we refer to as "canonical" Bartitsu, which is the collection of about 40 jujitsu kata and walking stick defense sequences detailed by Barton-Wright's articles.
Obviously, since he didn't record the whole art, the canon is incomplete, so we've also developed "neo-Bartitsu", which refers to cross-training and pressure testing "experiments" between 19th century "British jujitsu", old-school scientific boxing or fisticuffs, low kicking and the Vigny style of Swiss stick fighting. The idea is to continue Barton-Wright's work in progress, rather than to fully recreate the original art of Bartitsu.