A non-empty subset S ⊆ V of the vertex set of a simple graph G = (V, E) is called an independent dominating set if every vertex not in S is adjacent to at least one vertex in S, and no two vertices in S are adjacent to each other. The independent domination number of G, denoted by γi (G), is the smallest possible size of such a set. The independent domination stability (or simply id-stability) of G is defined as the minimum number of vertices that must be removed from the graph to alter its independent domination number. In this paper, we explore various properties of independent domination stability in graphs. Specifically, we establish several bounds and determine the id-stability for certain graph operations involving two graphs.