Let us model the poop rule as a predicate keep that maps the set of real world objects to {true, false} and a function poopy that maps the set of real world objects to the set of real world objects with poop on them.
For all x, keep(poopy(x)) = keep(poopy(poopy(x))), thus we can say that poopy is idempotent under keep.
Further, poopy is injective because there exist distinct x and y such that keep(poopy(x)) ≠ keep(poopy(y)). The proof by example is that you would keep a poopy million dollar bill, but you would not keep a poopy poop.
Your model is lacking in one area - poopy() has an inverse poopwash() where for some set of poopy objects Y, poopwash maps Y to a subset of the set of real world objects, but there exists a set of poopy objects Z for which poopwash maps Z to a subset of poopy objects.
My initial instinct was to suggest that for all z in Z, keep(z) = false, however I believe your million dollar example runs counter to this. Nonetheless, I suspect there is a useful subset of Z, let's say S, for which we can say, for all s in S, keep(s) = false.
It mostly depends on the surface of the item, not its value. Clothes and anything lined in fabric is gonna be toss, but you'd just replace it. Most things made of metal or are very glossy will be kept.
I would just throw clothes into the washing machine and maybe set it to a more thorough setting. Fabric lined would be a small steam cleaner with some enzyme cleaning spray until the water was clear and the staining was gone.
I've cleaned up too much dog poop to be overly concerned at this point.
By this logic, get rid of all your food and clothing. You can't get poop stains out of most clothing and obviously you're not going to risk eating food that had poop on it.
Also, go ahead and keep your litter box tools forever.
A few years back I was away for a while and came back to a nasty mouse infestation. When faced with the prospect of deep cleaning and sanitizing items, it made it WAY easier to get rid of stuff that I didn't CRITICALLY need.
Anything important I put in the work, anything not got tossed. I was able to cut back significantly.
Also gave me an excuse to spend a bunch on storage - everything is now stored in clear sealed plastic bins with labels - and left me with enough trauma that I'm now quite vigilant about cleaning :P
I had a similar situation with a mould infestation, and I agree that a side effect of something like that is that deciding what to keep and what not becomes generally easier, what it doesn't help with unfortunately is the actual task of sorting, which with executive dysfunction and chronic fatigue is a mountain of itself 😭
Do people hoard food? I suppose preppers, but they aren't likely to want any kind of method to decide what to get rid of. Plus, if you do decide to you can just stop buying food and eat your hoard.
In this world, people declutter their house not by silly things like: sentimental weight, utility, or decoration. But by if its had shit on it. Yes my dented pan has been shit in, and my used vitamin bottles may have been pissed in, but not shit in so its staying right where it is.
Interesting... I can't think of a single non-disposable thing that I wouldn't clean rather than throw away though, so maybe I only have good stuff??
I mean I've got some magazines that would be awful to clean, but I'll get around to reading them eventu--oh omg it works. I'm recycling my old magazines!