When the live wire in a branch circuit breaks, the only path for current is severed. Anything prior to the fault continues to function as designed, anything past the fault does not function at all.
In a ring circuit, there are two paths. When the live wire is severed, only one path is broken. The other path continues to function, but it is now able to draw current greater than what the wire is capable of carrying. Everything on both sides of the fault will continue to function, but not as designed.
When the live wire in a branch circuit breaks, the only path for current is severed. Anything prior to the fault continues to function as designed, anything past the fault does not function at all.
In a ring circuit, there are two paths. When the live wire is severed, only one path is broken. The other path continues to function, but it is now able to draw current greater than what the wire is capable of carrying. Everything on both sides of the fault will continue to function, but not as designed.