> “Seven! Isn’t it bad enough to think of killing one person? And in any case . . . bad enough to divide the soul . . . but to rip it into seven pieces ...”
> Lord Voldemort has seemed to grow less human with the passing years, and the transformation he has undergone seemed to me to be only explicable if his soul was mutilated beyond the realms of what we might call ‘usual evil’
Horcrux was to backup the soul and I believe any one fragment is enough to allow for recovery.