Is it permissible for a brother to refuse to pay a debt owed to his brother, which the latter spent on him to enable him to work and become stable? And does he incur a religious sin by neglecting the care of his parents and fulfilling their needs, despite his ability to do so?

The question boils down to two points: reclaiming the money spent on the brother, and demanding his help in caring for the parents.

It is imperative to be kind to parents, especially in their old age, in accordance with Allah Almighty's saying: "And to parents, do good," and His saying: "So do not say to them, 'Uff,' and do not repel them, but speak to them a noble word."

Regarding the reclamation of funds: If a person spends on another a non-obligatory expenditure according to Sharia, he has the right to reclaim what he spent if the recipient has money that the spender knows about. However, as long as the brother did not have money at the time of the expenditure, it is not permissible to seek its return from him. Nevertheless, he should have acknowledged the favor and reciprocated it.

As for the care of the parents, he bears the same responsibility as you do.