And you're quite right that the threshold for IB/ESA has been changed.
It used to join up with with the JSA threshold. If you were over the threshold but not in work, you got JSA. If you were under the threshold, ie your ability to work was significantly compromised by illness, you could get IB. (NB some people under this threshold were able to earn their living anyway, but only because a suitable role was available.)
The safety net has now been rolled back so that there is a gap between being well enough to be employable and being ill enough to get IB/ESA. And people are falling in the middle.
There are documented cases of people being refused both, but here's a thread that caught my eye on MN.
In this case, the employer has offered reassignment and the employee refused to take it, so in this circumstance the employer seems in the right.
But it's easy to see there will be plenty of people at that level of illness. They pass the DWP threshold of being able to work - sometimes they actually do work. But they doesn't pass the threshold of being able to do the job. They may not be able to deliver in any fulltime, earning-a-living job.
People at that level of illness will end up long-term unemployed - possibly for the rest of their lives - because they can't deliver what employers want. But they'll be treated by the DWP as ordinary unemployed and subjected to penalties and Mandatory Work Activity. So because they can't do a sitting down job for real pay, they'll be told to stack shelves for workfare. And when they fail to do this, even the JSA will be removed as punishment.
This is why disabled people are screaming. It's not for fear of loosing our flat-screen tellies.
It's because the design of the new system predictably makes some vulnerable people destitute.