Because she's doing 16 hours, she could declare it, come off JSA and get working tax credit. She'd then be exempt from the benefit cap and her housing benefit (if she gets any) would go up. She could be significantly better off.
If she's on ESA, she could ask for permission to do permitted work (you have to fill in a form PW1, which might be available online) and she could work up to 16 hours pw and earn up £120 without losing any benefits at all.
On UC, she should (in theory) be better off in work, but I'm not sure how it works in practice because we're practically the last place in the country to get the full rollout, so I haven't had to find out just how it works yet.
I agree that what she's doing is wrong, but I totally get why she's doing it. Any change like that seems to fuck up people's benefits for months while DWP reassess everything, and if it's cash in hand cleaning it's hard to provide evidence that will satisfy them.
When I work with big families that are benefit capped, the first thing I do is check if any of them have health issues that might entitle them to PIP, or DLA for the children. Anyone in the family getting either means that the benefit cap doesn't apply. One of my clients has just had arrears payments of well over £3k (DLA, CTC and HB) because we got DLA for one of her DCs.
The benefit cap is just cruel imo. Someone I know loses a small fortune, she has just 2 kids and is in a housing association property but she still lost about £90 pw.
It affects people in the south-east but outside London disproportionately because rents are so high here.