I have been working professionally in aviation for the last decade either as a pilot or a maintainer. That said, generally aircraft with a malfunction that could negatively effect passengers or crew members in the event of an emergency would not be cleared to fly. However, there are waivers/authorizations to fly with a know malfunction in order to move the aircraft to a location where maintenance can be performed or like another member said, to conduct a Functional Check Flight (test flight to ensure all systems are working like they should, but these flights can be tailored for specific malfunctions and do not require an entire check of all systems if the malfunction/broken piece is identified). Either way, if the problem is fixed or is in the process of being fixed...we are seeing progress. Go BLTA!