How can I create a bootable USB drive for a laptop I can't boot?

I have two old MacBook Airs: one from 2011 and another from 2015. The 2015 Air boots fine, while the 2011 gives me the flashing folder missing system icon on boot. I tried booting it into recovery mode, and it asks for a password, which I'm as near to 100% sure I have correctly, but when I enter it and press return, the password field clears and nothing else happens. So I thought I'd use the 2015 Air to create a bootable USB drive with High Sierra on it (the latest OS the 2011 will boot, according to MacTracker). Plugging this into the 2015 Air while the Option key is held down correctly gives me the choice to boot from the internal or the USB drive. However, doing the exact same thing on the 2011 Air gives me the useless password screen. Not holding the option key down (hoping that, failing to find an internal boot drive it'll look automatically for an external one) brings up the flashing folder. I'm guessing perhaps that creating a boot USB from the 2015 won't necessarily work on the 2011. Or maybe the 2011 is simply a brick now. Is there anything to my theory about the 2015 not creating a correct boot drive for the 2011? Is there anything I can do to bring the 2011 back to life by installing a new OS on it somehow?