The machine is precisely calibrated so that the circumstances of the person's simulated life are such that it will maximize their happiness. — Count Timothy von Icarus

Simply assuming a machine has already solved a philosophical problem, such as what is happiness in this case, doesn't really solve all that much.

In "The Consolation of Philosophy," Boethius argues that happiness is equivalent to being good, since virtue is what leads to happiness. He believes that true happiness is not found in external circumstances, such as wealth or power, but rather in the internal state of the soul. — Count Timothy von Icarus

Taking this as the definition of happiness, the machine does absolutely nothing.

The whole foundation of stoicism, the philosophy which Boethius represents in the Consolation, is that true goodness cannot be dependent on anything external, such as the machine.

The answer to your question is that the machine does nothing with respect to happiness, goodness, or virtue; those are internal qualities of the soul and do not depend on anything external whatsoever, including the machine.

As others have pointed out, perhaps the machine is a useful training tool that a good person would use to increase their skill at some set of tasks, to then do those tasks more effectively later. I.e. just an analogue for education and training generally speaking.

However, education and training are external circumstances in the stoic framework. The slave, defined here as someone who lacks everything, and the emperor, who possesses everything, are both morally equivalent in their capacity towards the good; the greater means available to the emperor, including for example a virtue machine, changes nothing.

A good emperor would use a virtue machine to do good, and a bad emperor would use it to do ill.

Generally speaking, anything that is contingent on external events (such as access to books, discussion, training regiments, virtue machines) has no intrinsic moral worth in the stoic system. Of course, a good person would make good use of such contingencies but that does not make them any morally better than had they been deprived. A good person will use plenty to do good but would do an equal amount of good in complete lack: equal amount of effort towards the good, just the results would be less visible having no or little effect on the world provided zero means.

These basics of stoicism and the Consolation being understood, if the question is then what would a machine "programmed for stoicism" do, the answer would be to provide the user of the machine a choice of what the machine is capable of; i.e. some sort of training that would in some calculus be more effective over projected lifetime than going without it.

Whether the user could leave or not does not really matter.

If the occupant can leave, then when the occupant has decided the benefits of the machine are outweighed by the benefits of returning to the world and applying what was learned, the occupant would leave; if the prisoner could not leave then the prisoner could continue their effort towards the good and truth assuming it is useful in the next life.