This analysis is wrong. One inherits the debts, but only up to the value of the assets inherited. See Art. 1.792

Art. 1.792. O herdeiro não responde por encargos superiores às forças da herança; incumbe-lhe, porém, a prova do excesso, salvo se houver inventário que a escuse, demostrando o valor dos bens herdados.

Free translation:

Section 1792. The heir is not liable for charges greater than the forces of inheritance: it must, however, provide evidence of excess, unless there is inventory to excuse himself, demonstrating the value of inherited assets.