Interesting aspect, does anyone actually know which "link in the system" is by design the weak point of the Carabiner type?
I suspect that might depend on the type used? Al-Ko use a hook that you have to close onto the handbrake's hole, whereas some non-genuine ones use a "key ring" link.
See PC article on fitting replacement cable
I have only seen two breakaway cables that were used as intended, both had failed at the dog lead clip, but I never knew if the owners ever looped these as intended or not.
I have not seen a "used" carabiner type to note where this had failed, a genuine or non-genuine one.
Intuitively I would suspect it is unfolding the swaged-on hook, at the handbrake bottom end that you close to form an eye, on fitting.
LINK to genuine Ak-ko product. Or simple unravel the keyring type.
I have only once needed to ever fit one, a genuine Al-Ko one, closing the hook was challenging but achieved with a genuine Mole grip. [because a wire strand had broken loose in the looped area, and I thought I ought to replace it]