It tends to occur in persons with a hypercoagulable state (Trousseau's syndrome, a paraneoplastic syndrome associated with malignancies) and in very ill persons.
So when either of these proteins is deficient, it leads to a hypercoagulable state, meaning a person is at increased risk of developing a clot that could block blood flow.
All right, as a quick recap, protein C and S deficiency refer to two separate hereditary hypercoagulable disorders that involve the inability to inactivate factors V and VIII in the coagulation cascade.