The present technology is directed generally to devices, systems, and methods for enclosing anatomical openings. In several embodiments, an aneurysm device is endovascularly deliverable to a site proximate to an arterial aneurysm. The aneurysm device includes 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 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. In some embodiments, the device can also include a barrier spanning at least a portion of the distal-facing aspect of the closure structure and configured to further occlude a neck of the aneurysm. In further embodiments, the closure structure can be configured to restrict and/or divert flow to or from the aneurysm.