Can you contract HIV without having sex or drug use?
Yes. It would be incredibly unlikely, though. HIV is transmitted by direct fluid exchange. Somebody's blood, semen, vaginal or anal-mucosal fluids, or breast milk need to enter your body in order for you to become infected. Obviously, those fluids would have to come from a person both infected with HIV and with a significant amount of HIV in their blood. Once their fluids leave their body, the HIV in them does not survive longer than momentarily, except in syringes which shelter blood in liquid form. That's why sex and IV drug works account for almost all HIV infections, other than prenatal and birth or breastfeeding infections. Yes, it's theoretically possible for infections to take place when two people are actively bleeding and HIV-bearing blood from one person enters the other person's wound. In the entire history of the global pandemic, however, reports of that kind of infection have not exceeded a small handful. Accidental needle sticks in a medical setting can endanger health care professionals but again, the risk is really small. That almost never happens because needle sticks without injection present only a tiny risk of infection. Fresh, HIV-bearing blood, semen, or vaginal fluid in an eye could also present a small risk. Best avoided if possible. In general, however, we can observe that almost all HIV infections result from anal or vaginal sex, or from sharing IV drug works.