This study will test the safety and blood levels of the antibody BNT351 in people living without and with human immunodeficiency virus (HIV). This study will also test the anti-viral activity of BNT351 in people living with HIV (PLWH) with detectable virus levels. The main goals of this study are: * To learn about the safety of BNT351 and check for side effects. * To measure the amount of BNT351 antibody in blood over time. * To test the amount of HIV in the blood at different times after treatment with BNT351 in people living with HIV.