Sounds like droit du seigneur (right of the lord) or jus primae noctis (right of the first night), the supposedly legal right of medieval lords to have sex with socially subordinate women on their wedding nights. Similar customs are referenced in ancient, medieval and later times. It's mentioned in Shakespeare. It was banished in Spain in 1496.
Not exactly the same, but another interesting practice concerning the wedding night comes to mind. In many countries, it was required that the consummation of marriages be witnessed, especially among -- though not restricted to -- royalty. It's called the bedding ceremony. One imagines bleachers and pom pom girls rooting the couples on. One controversial example was that of Prince Arthur, eldest son of Henry VII, and Catherine of Aragon in 1501. In the morning, Arthur wobbled out of the bedchamber, claiming he had spent the "night in Spain". He died four months later and Catherine wedded his younger brother, the future Henry VIII. When their marriage failed to produce a male heir, Henry tried to dissolve the marriage on the Biblical stricture that one may not marry his brother's wife. He gave the bedding ceremony as proof that the first marriage had been consummated, an assertion which Catherine vehemently denied. It sounds delightful, until I remember that the first attempts of my current wife and myself were, despite our sexual experience, not altogether successful; it took us awhile to relax and achieve, shall we say, the perfect fit.
As to the OP's proposal, I ask, "Cui bono?" Who benefits from another man screwing your wife before the wedding? Not I; the guy doesn't get to sample other women. Since I'm hung like a chipmunk, supposedly my wife would. However, she'd sampled many men before me, most reportedly better-than-adequately endowed, and still chose little ol' me. On the whole the suggestion sounds like a form of premarital cuckoldry, ideal for those guys who'd just love to speed the whole thing up.