The present technology is directed generally to devices, systems, and methods for enclosing anatomical openings. In one example, an aneurysm device is endovascularly deliverable to a site proximate to an arterial aneurysm. The aneurysm device can include a closure structure having a distal-facing aspect configured to at least partially occlude the aneurysm and a proximal-facing aspect configured to arch over lumina of an artery. The closure structure can include a plurality of struts forming support arms and anchoring arms. The device further includes a supplemental stabilizer connected to the closure structure and configured to reside in the artery and press outward against a luminal wall thereof. A barrier can span at least a portion of the distal-facing aspect of the closure structure and be configured to further occlude a neck of the aneurysm. The closure structure can be configured to restrict and/or divert flow to or from the aneurysm.