I know that hpv can leave the body in few years with immune system. what stds also can leave the body & what doesn't ? and why if possible??

It's complicated...: Even without treatment, some STDs are cleared in a few weeks or months, such as gonorrhea and chlamydia. But they still need treatment; they can leave a lot of damage if not treated. HPV is cleared, but it usually takes 1-2 years, and HPV DNA persists and infection can reappear. STDs that last indefinitely include syphilis, herpes, hepatitis B, HIV. The biological reasons are complex.