WasabiTillyMinto I'll share a weight loss story,just for you ;)
A while back, I had 2 young children and there was no work about where I lived, none at all (quite rural area). So we took a risk and moved cross country to where ExP grew up as there was some work going there. It swallowed what ottos savings we had to move, but we had to go where the work was, so did it. There was no subsidised housing (thanks for that, Maggie) and HB didn't cover all our rent. For 6 months,we got by and did ok, albeit on a payday to payday basis, then ExP lost his job due to the company folding. It took over a year before he found anything else. During that year on benefits, after paying bills (metered gas and electric and rent top up) we had £23 a week to feed 2 adults, 2 toddlers and a dog. We got some help with the odd delivery of dog food from a local charity but couldn't rehome her as we had rescued her when the RSPCA were unwilling unable to step in, and she had some issues. She would have been put down if she had gone to a shelter.
During that time, I often went without or just ate the kids leftovers. My weight went down to just over 6 stone. I am average height. At one point I had a living room of coppers who were trying to raid the junkie next door but due to some admin snafu had a warrant with our address on it, so I had them in to sit down for a cuppa while they tried to get a new warrant sorted. One of them saw a family photo on the wall of me with DS2 just after he was born, so carrying the baby weight still, and commented on the weight loss. He suggested that maybe the snafu wasn't a waste of time after all as they could just have a look round my house for whatever had caused me to lose so much weight. So not only did I look like Skeletor's ashen faced sister, apparently I also looked like a junkie 
Now consider that this was almost 10 years ago. Benefits have risen slightly in that time but food costs have spiralled. Back then I could get a loaf of bread, 3 tins of beans, pack of pasta and 3 tins of tomatoes for less than a quid. At a push, that is 6 meals. Now it is more than 30p just for one tin of tomatoes.
I don't recall the exact numbers, but I read something recently that said that 15 years ago a weeks JSA would buy you 187 loaves of bread. Today it would buy you 45 loaves. So no, I don't find it hard to believe that people are struggling to find money to eat at all, let alone well. If that is a long term situation for someone then of course they are going to lose weight. The longer it goes on, the more they will lose until they reach the Skeletor stage.