You clearly don't know the system at all, you can claim either ESA or UC but not both, she was clearly not well enough to manage her benefits claims and the DWP are meant to have systems in place to help vulnerable clients, including those with schizophrenia, but they obviously didn't work here.
It looks like her PIP was stopped because she didn't fill in a form and DWP should have been liaising with her mental health team so that didn't happen but it looks like they also failed her.
The worst case I saw in welfare rights work (before UC) was a man with schizophrenia who had failed his assessment to be eligible for sickness benefits and told to sign onto JSA instead. When he tried this he was told he was too unwell to claim JSA. By this point he was being threatened with eviction and his electricity had also been turned off.
I also know of one man with schizophrenia, the day hospital noticed he was getting thinner and thinner and asked him why and it turned out he had been fit for work and had no money so his only meal had been lunch at the day hospital monday to friday.
There are so many people who fall through the cracks that stories like this don't shock me any more.