BGP best path - which behavior when best selected path is lost?

Hi there,

I got a question about BGP for which I still haven't found a satisfying answer.

Suppose a BGP peer (e.g. a route reflector) receives multiple advertisement about a prefix, each from a different advertising peer (but same originator) from which the best one will be selected by the algorithm.

Suppose the said BGP peer no longer receives the specific advertisement that was selected as best path, but the next hop hasn't failed, the advertisement of that path has only been stopped (e.g. a peering went down)

What happens to its peers, the ones that were receiving that best path from the said BGP peer? Will they receive the second best path instantly from the said BGP peer? Will there be a delay or traffic disruption?

Thanks for your help!