Originally, the US constitution specified that the runner up to the president in the electoral college becomes vice president, which would currently be Hillary Clinton instead of Mike Pence. This was abandoned in 1804 in favor of the current system where there is a separate vote for vice president.
I'm curious to know whether the original method of electing the vice president is unique. Are there any other electoral systems (either historical or currently in use) where the runner up is officially recognized or given some power? In particular, is there any other system where the runner up succeeds the winner if the winner is unable to serve? The VPOTUS system was unworkable, so I'd be particularly interested in any similar system that ended up working well.
The closest I can think of is the leader of the opposition in parliamentary systems. However, this position usually has no power, does not succeed to the prime ministership, and that person must still win their own seat in the legislature.