This "chaos cycle" is executive dysfunction. I see it a lot supporting people with ADHD online. It's extremely destructive.
If you have poor executive functioning skills (which are not only caused by ADHD, it can also be things like FASD, PTSD, general low IQ/learning difficulties, severe depression, epilepsy, acquired head injury, drug or alcohol abuse, among other things - some of this can be caused by the results of childhood neglect as well) then you will struggle to maintain habits and routines or to think ahead and anticipate/plan for the future. People who struggle with executive functioning tend to have poor impulse control and essentially live very much in the moment with a sense of not really being in control and feeling that things just happen to them.
This has a knock on effect on the environment because of things like disorganisation, but also because of decisions that have been made where the consequences haven't been thought through like getting a pet for example.
That disorganised environment then makes it even harder to maintain habits, routines, or meet basic needs like feeding or cleaning yourself, let alone more complex tasks like helping children with homework or performing household maintenance. And it may make you feel depressed, hopeless or ashamed. All of these things in turn make executive functioning worse, contributing to further degradation of the environment which makes the problems worse etc etc in a kind of downward spiral.
Any attempt to fix any part of it is usually short-lived due to the fact that maintaining progress requires a fair amount of executive functioning but also because there are so many issues adding to the chaos that trying to solve one area of chaos feels like shovelling snow while it's still snowing. Or because they are trying to fix everything at once and this is impossible so they just fix little bits which get instantly undone and the whole thing feels hopeless. You can go in as an outside helper, with a metaphorical snowplough and clear a whole area but because of the executive dysfunction it will be full of chaos again within a day or two. A clean slate doesn't stay clean unless you can address the underlying problem.
There are some things which do help though. Appropriate medication for any conditions e.g. ADHD or epilepsy and possibly mental health conditions can help a lot. I would strongly suggest anyone in this cycle ought to be referred or at the very least given a screener for ADHD (the ASRS is the usual one). Understanding what executive functioning is and how it affects day to day life can be really helpful because that makes it clear what needs to be externalised (e.g. time cues).
Breaking the above cycle means breaking the chaos down into different areas (e.g. laundry/sleep/food/routines) and working solidly on one at a time, understanding that while you're working on the first couple you're not going to see any real results from this because you're only taking away one "snow cloud" but the other 99 are still snowing. You do start to get progress once you've cleared a few, which starts to slowly lift the burden on all of the other things but it takes time and sustained effort at one thing, not a lot of random, uncoordinated efforts at different things. And most people need moral and/or practical support during this process because it can all start to unravel very quickly.