Interesting ideas PoP. I hadn't considered those. However, I see
a flaw (in the case of my own bin anyway).

Any sort of strengthening rib would have to go half way down the
bin as that's where I get most deflection. I don't have a problem
in the upper part near the lid.

Whether the rib is horizontal (i.e. a hoop) or there are multiple
vertical ribs, if they are inside the bin then they are going to
interrupt the airflow in a place that is important for the
functioning of the cyclone effect.

You may find that the bin still works but less efficiently.
That's OK if your modification is easily reversible.

If you mount them outside the bin, any residual delfection may
eventually work the bin loose of the glue holding it to the rib.
Strnghtning it it in some way (self tapping screws though from
the inside?) may work or you may get material fatigue after a
while. Still, if the bin is only a fiver you can afford to
experiment.

Interrupted air flow is why I rejected one obvious valve design:
a rod attached to the outside of the inner blucket and sticking
out radially so that it enters a short rigid tube (say 20mm +
diameter) attached to the outer wall of the bin. If the rod ends
just inside the outer mouth of the tube, then when the bin begins
to collapse it will quickly emerge from it. If the mouth is
covered with some sort of weakly spring-loaded cap, under normal
conditions no air will be admitted, but as soon as a collpase
starts the cap will be forced open by the emerging rod.

This is a visually neat and easily implementable idea that may
work, but even if it does, the rod will introduce turbulence into
the cyclone air flow and therefore isn't too desirable from that
point of view.

My current idea is to use the initial bin deflection as a
trigger, but the mechanism will be external. I have refined it
down to a fiarly minimal form. All I have to do is find time to
make it! Hopefully within the next week.

The advantage of a valve is that it maintains air flow through
the vacuum. The motor may overheat if a blockage is allowed to
persist.

W.