After taking antibiotics sputum production often lessens or "dries up" for a while. Is your husband nebulizing with saline for airway clearance? I don't know his diagnosis but if he had Pseudomonas I suspect he has Bronchiectasis and should be doing airway clearance. Airway clearance practices involve a number of different practices to be used that help keep damaged airways clear. Any of these can be done in order to help produce a sputum sample for testing.