This is actually pretty straightforward. The toxin is targeted at a critical organ or function, and the "antidote" is not actually an antidote, but rather provides the same effect as the now-missing organ.
A simple example would be a toxin which comprehensively destroys the Islets of Langerhans, while the "antidote" is insulin.
A slightly less common case would be thyroid/thyroxine. In fact, Dorothy L. Sayers wrote a Lord Peter Wimsey story, "The Incredible Elopement of Lord Peter Wimsey" about a sadist who punishes his wife's possible infidelity by withholding her thyroxine tablets (she has hypothyroidism) for long periods, turning her into a cretin.
EDIT FOR THE SAKE OF HONESTY - Sayers was either mistaken or taking literary liberties. Hypothyroidism in adults does not produce cretinism. It's a developmental issue, so my example is not actually correct. But I enjoyed the story a great deal, so I won't delete it.
There is, of course, a drawback here - these conditions are known and the counteracting medications readily available. Here is where authorial license comes in. There are any number of brain functions which might be controlled by an as-yet-undiscovered chemical. Oliver Sacks has written an excellent book "Awakenings" about sleeping sickness patients whose condition was caused by dopamine deficiency, and feeding L-DOPA (a dopamine precursor) made amazing improvements. At least temporarily. Likewise, destruction of the substantia nigra (or at least dopaminergic neurons in the pars compacta) produces Parkinson's. A toxin would be asserted to be able to destroy some critical function, and the prison (or more probably the central government which administers the prison) is in possession of some secret therapeutic material which will provide function.
EDIT - It has been suggested that I address the possibility of recovery. I see at least 2 possibilities.
The first is that the damage produced by the toxin is temporary. With supportive treatment the affected function will recover. To put it a bit inaccurately, it's not the disease that kills, it's the symptoms, and if you keep the symptoms from killing the body will eventually recover from the disease. An example might be tetanus: the cause of death is not organ destruction, but rather asphyxiation or heart failure due to sustained muscular contraction. Keep the blood oxygenated and the patient will (probably) recover. Another example would be the Milwaukee Protocol for rabies, in which the patient is put in an induced coma to prevent (more or less) brain damage while the immune system gets control of the virus. Note that this example is iffy - one study suggests an expected 8% success rate. At any rate, in this version of things the replacement medication only needs to be continued for a limited duration. Of course, this implies that the toxin will need to be readministered at regular intervals if Joe is expected to be a prisoner for a long time, but frankly I don't see this as an overwhelming problem. Joe is, after all, a prisoner and at the mercy of the EO.
The second possibility is as straightforward as the original suggestion: transplant. One experimental therapy for neurological conditions such as Parkinson's is the transplant of fetal brain tissue, which is hoped to replace reduced function in the affected portion of the brain. The author can have any amount of fun developing the mechanism and pitfalls of the process - compatibility (note that fetal tissue is somewhat different), sources, recovery therapy,etc).