The petroleum prospectivity of an exhumed basin is largely dependent on the ability of pre-existing traps to retain oil and gas volumes during and after the exhumation event. Although faults may act as lateral seals in petroleum traps, they may start to become hydraulically conductive again and enable fluid flow and hydrocarbon leakage during fault reactivation. We constrain the present day in situ stresses of the exhumed Illizi Basin in Algeria and demonstrate that the primary north–south and NW–SE (vertical strike-slip) fault systems in the study area are close to critical stress (i.e. an incipient state of shear failure). By contrast, the overpressured and unexhumed Berkine Basin and Hassi Messaoud areas to the north do not appear to be characterized by critical stress conditions. We present conceptual models of stress evolution and demonstrate that a sedimentary basin with benign in situ stresses at maximum burial may change to being characterized by critical stress conditions on existing fault systems during exhumation. These models are supportive of the idea that the breaching of a closed, overpressured system during exhumation of the Illizi Basin may have been a driving mechanism for the regional updip flow of high-salinity formation water within the Ordovician reservoirs during Eocene–Miocene time. This work also has implications for petroleum exploration in exhumed basins. Fault-bounded traps with faults oriented at a high angle to the maximum principal horizontal stress direction in strike-slip or normal faulting stress regimes are more likely to have retained hydrocarbons in exhumed basins than fault-bounded traps with faults that are more optimally oriented for shear failure and therefore have a greater propensity to become critically stressed during exhumation.