Will the airbag deploy if the airbag light is on even by malfunction or does it mean the airbag is just not connected?

Will the airbag deploy if the airbag light is on even by malfunction or does it mean the airbag is just not connected?
It depends on the make and year of the vehicle. Some manufacturers develop systems that will shut down the airbag if a fault is found, some will just shut down a part of the system (say one airbag in a multiple airbag system), some will not shut anything down but just alert you that there is a problem. Please don't try to service the airbag by yourself, they can cause serious injury if set off unintentionally. Also if the airbag is set off, sometimes it is more expensive to repair the system than the vehicle is worth, that is why some insurance companies will total a car if an airbag is deployed even if only minor cosmetic damage is sustained. See your vehicle dealer.