One exemplary device includes a tubular structure having proximal and distal ends and at least one layer of braided material configured to facilitate thrombosis. The tubular structure includes an end section at the proximal or distal end having a cross-sectional dimension that is larger than that of an opening of the target site. The device also includes a stiffener wire coupled to the tubular structure, and the wire is configured to extend at least partially through the opening and facilitate securing the end section over the opening. The tubular structure and stiffener wire include respective preset, expanded configurations and are configured to be constrained to respective reduced configurations for delivery to the target site and to at least partially return to their respective preset, expanded configurations at the target site when unconstrained.