<p>This note is concerned with stability of linear variational inequalities (VIs) in Hilbert space. We prove an asymptotic global convergence result under appropriate conditions for perturbations of all data of a linear VI, that consists of a linear operator, a right hand side, and a convex constraint set. Here we employ Hausdorff set convergence to handle perturbations in arbitrary closed convex constraint sets what is a main novelty of the paper. To provide a simple illustration of our abstract stability theory we consider a VI of Volterra type with memory term and with unilateral constraints on some time interval and a box constrained variational problem involving Fourier series. We derive asymptotic global stability results for these variational problems.</p>