Radiation Island can be played in two different modes. The mode you select will determine what happens to your currently equipped weapon when you are killed.
If you choose to play Adventure mode you will be selecting the more difficult of the two modes as you will have to deal with the game mechanic of losing your currently equipped weapon upon death. There is a simple way around this though and that is to unequip your weapon once you know you are close to dying.
If you decide to play Exploration mode you will not have to worry about what happens to your equipment upon dying as you will retain everything for your next playthrough.