The invention relates to a turbine engine exhaust casing (1), characterized in that it comprises: a hub (2), an outer ring (3); a plurality of structural arms (10) arranged circumferentially between the hub (2) and the outer ring (3); a stiffener (11) extending along at least a portion of the inner circumference of the hub (2), the hub (2) comprising at least one discharge hole (15), and the stiffener (11) comprising at least one discharge slot (16), so as to enable the discharge of a fluid from the casing (1). The invention also relates to a turbine engine comprising such an exhaust casing.