The salt will be dissolved by the next rain shower, or by meltwater (e.g. if the salt has been put onto snow), and drain away. Where it ends up depends on the location.
If the verge is grassy, or made of other porous material, like gravel, then the salt solution will soak into the soil, where it will presumably remain for a while, but further precipitation will sooner or later cause it to percolate through to the local water table. From there it may end up in the nearest waterway, or, if it reaches an aquifer, some may and up in our drinking water.
If the verges are hard, with a gutter and drains at intervals, the salt solution may be channelled into the nearest watercourse or it may reach a watercourse (or the sea) via a sewage works.
Whatever route it takes, the vast majority will end up in the sea eventually.
