I don't know the particular scenario in question here, but if the breadcrumb is too long to be shown in a single line then there is already too much information for the user to care about and you should consider simplifying what is displayed, not trying to find a way to squeeze more information than necessary into a space that is not big enough to hold it.
By adding sliding functionality, you would be over-complicating a mechanism which is meant only to serve as an aid alongside the primary navigation structure.
One common reason for breadcrumbs to become very long is that the text for the elements is taken from a source that was never designed for breadcrumbs, such as the titles for pages or faceted navigation or the primary navigation itself, including mega dropdowns.
I'd really suggest removing the problem rather than expending effort to incorporate the problem because then - you'll have two problems.