Can there always be some sperm in precum or just in those cases when it is left after previous ejaculations?

Never can tell: Sometimes there will be sperm before an ejaculation. There are likely always sperm after an ejaculation. The rule is, fertile couples who have sex will have babies... at some point, but maybe not the first time they have sex, nor the second,... but it will happen. That is why a good Plan A, a reliable birth control method, is needed all the time. Of course, not having sex means no babies.