A lockable military duffle or sea bag is good. Except they can be easily cut. Add pacsafe for some protection. I like a duffle bag with a D shaped main opening like a foot locker for organization. If I'm really serious about needing this type of set-up, the D-shaped main opening bag, inside a pac safe inside the military duffle. Yes, this adds a lot of weight, but the "only" reason I can envision something like this is going to a shelter, even if it's only to church temporarily (in an emergency, it's likely not everyone there will be a member or even known to anyone). I'd rather a lockable metal footlocker for this scenario (or my old military wood one) and hopefully unobtrusively chain it to something immobile. My dog(s) like laying on and next to these. In a pinch, put the bag or foot locker inside a large, locked dog crate with a dog. This also works for BOBs.
Wheels are necessary for me to move this, so strapped to a heavy-duty cart, wagon, or wheel barrow for movement unless someone is helping. Most of the bags with integrated wheels don't do well in deep snow or deep mud, so not a good choice for where I am now.