Nothing really happens to the B1/B2 visa. When entering the United States, the purpose of visit decides which visa should be linked to the newly issued I-94. If you are entering for a job, the H-1 visa is linked, if purpose is tourism or short business visit, then the B-1 visa is tagged. US consulates abroad do have a system where they ‘cancel without prejudice’ but this applies when you have a stamped F-2, go to your home country and then get an F-1 stamped. Then the F-2 will get cancelled. Same for H-4 stamp that will no longer be valid when you get an H-1B stamped. B-1/B-2 and H-1B are not in the same class, group or category; so both visas will survive on a passport.