For non-rogues this convenience option makes the box stay in Buffomat indefinitely until it's either turned off or the locked box is removed from inventory. For rogues it also doesn't attempt to unlock the box but that's a separate feature request :-)

Perhaps a sub-checkbox called "Ignore locked containers" or something.

Confusing. I often have locked containers on my non-rogue characters, and this never triggers an "open box" task in Buffomat.
How do I reproduce?