I store my open but not currently used rolls of filament in a large plastic tote with a gasketed lid. I guess you could call this a "dry box," but it's not very heavy duty. I have a stocking full of silica gel desiccant beads in it, the kind that change color when they're allegedly saturated. I nuke that in the microwave about once every six months. They're never indicating their saturated color by then, but it pays to be sure.

Whatever roll is currently loaded in the printer I have in a heated filament dryer which can output right to the printer. Its lid is not sealed, per se, but it's not just open to the air, either. I run the dryer when I'm printing. That hasn't given me any issues.

In my environment -- a basement that's not terribly damp, and I leave a dehumidifier running maintaining an alleged 30% RH -- if I leave an exposed roll of PLA on the machine it will get brittle enough to potentially start snapping bits off within about 2-3 weeks of sitting exposed to open air.