When you're too unwell to work, but the DWP/Atos says you are well enough - because you can push a button - your benefit is usually stopped before you receive the decision letter. In this letter, you're told to apply for JSA. (Please note, the letter does not tell you that you can receive a reduced amount of ESA while appealing, if you send a medical certificate.)
When you go to sign for JSA, as instructed, the JCP asks you whether you're fit for work, as this is a condition of claiming. Your fitness according to the DWP itself does not count. If you're unfit to work in the real world (as differentiated from Atos world), you cannot legally claim JSA.
Thus, you are left without income by the DWP's own system. As soon as ESA or JSA are stopped, housing benefit stops too.
In another scenario, it's now been evidenced that JCPs are told to sanction a certain proportion of jobseekers' benefits. Consequently, claimants are having their benefits stopped for trumped-up reasons: a popular one is failing to attend an appointment you were not told about. Again, loss of JSA means instant stoppage of all other benefits.
Sick claimants, too, are being sanctioned for failure to comply with therapeutic or back-to-work programmes inflicted on them by so-called providers. ESA claimants have had their benefits stopped for not being able to get to an upstairs appointment in a wheelchair, failing to go to appointments they weren't told about, collapsing in meetings, being in hospital, and many other Orwellian 'crimes'. Loss of ESA means instant stoppage of all other benefits.
Social fund grants have been discontinued, leaving budgeting loans in their place. Budgeting loans are repaid directly from your benefits, in instalments. You cannot have a budgeting loan if you can't prove your ability to pay it back. If you're not getting any benefits and have an income of £0, obviously you're not able to provide this. You won't get a loan.
If poor decisions lead to destitution in this country, the unwise choice was probably "trusting the government"!