What is this type of car called?

Thanks guys,
Dare, ya I to realize that the roof and doors provide the strength.
However, if you put in s subframe and tie it all together nice and tight,
Would that not allow this?

Honestly, I tried to shave the drip rails and I am not to happy with how
It looks, so that's why I'm considering what my dad suggests.
Or just scrapping the car.

If you do this i would put in something stronger than the standard sup frame connectors.

Something like 3/8th wall thickness at the minimum.

But really, I don't think it's a good idea.