The motion of non-Brownian aerosols in an open laminar cavity flow is investigated by means of numerical and asymptotic methods. The cavity is a rectangular domain where air enters through an inlet located on the top, and exits in the horizontal direction through symmetric apertures near the bottom wall. While such flows are generally used to provide a clean (particle-free) environment, the introduction of any object inside the cavity can affect the flow topology and, in return, can lead to large aerosol residence times. In addition, it is known that the unsteadiness of the flow, though weak, significantly delays the exit of aerosols from the cavity. The goal of this paper is to analyze the conditions under which these phenomena occur, for heavy inertial particles with a small response time and a finite free-fall velocity, in a laminar cavity flow. A two-dimensional situation is considered and investigated by means of numerical simulations and perturbation methods, at moderate cavity Reynolds numbers. It is observed that any obstacle placed inside the cavity (along the symmetry axis) creates large quasi-steady triangular recirculation cells stretched by the outward flow, provided the Reynolds number is not too large. In particular, streamlines near the floor are reversed, so that deposited particles are swept inward and remain in the cavity. The probability of trapping has been calculated asymptotically, for inertia-free sedimenting particles, and compared to numerical results. Trapping in the wake of obstacles is observed to persist when the flow is slightly unsteady. In addition, it is shown that the small but finite unsteadiness of the flow can lead to the temporary trapping of a significant portion of particles by large recirculation cells near the upper corners of the cavity. This phenomenon takes place in spite of gravity and centrifuge effects due to the curvature of the cell, and leads to a long-term suspension which significantly increases the residence time of aerosols. By making use of separatrix map methods, the critical aerosol diameter below which this phenomenon occurs has been obtained and compared to numerical simulation results.