should airbag inflate when seat belt is NOT worn?

On most newer Toyota vehicles with the SRS system, they will deploy if the seat belt is not worn and there is a passenger of adult weight in the seat. Toyota designed sensors in the seat to detect weight. I hope I understood you correctly as to what you were asking.

The driver's side SRS should deploy whether or not the seat belt is worn. On the passenger side, it depends on the year and model.

In both cases, the SRS will only deploy if several parameters are met, like angle of impact, rate of deceleration, and whether the system is energized or not.

Isn't it more important for the airbag to inflate when the occupant is unbelted?

Several years ago, government crash tests were performed with the test dummies unbelted.

No. The occupant has to be wearing seat belts in order for the air bags to be effective. Without seat belts, the occupant may not be in position for the air bags to do any good, and may not even be in the car when the air bags deploy. In a high speed collision or rollover, there is a pretty high likelihood that an unbelted occupant will be ejected from the vehicle, making air bags useless.

I've read of deaths occurring even in 12 MPH colllisions in airbag- equipped cars when the occupant didn't wear the seatbelt, but in higher speed collisions, how is it safer for an unbelted occupant if the airbag doesn't deploy?

I did not say that it is safer for an unbelted occupant if the airbag doesn't deploy in a higher speed collision. What I'm saying is that in a high speed collision, an unbelted occupant will be seriously injured regardless of whether the airbag deploys or not.

There are people who do not wear seat belts so that they do not have to worry about escaping their vehicle if it stalls in front of a rushing train or the car is swept off the road by a tsunami and submerged.

And possibly crushed under the vehicle or run over by other vehicles. In many accidents, there are also other impacts after the airbags have fired.

Yup, that is a more common occurrence than most people realize.