There are several things the defense can do:
1. Bracket Coverage- This is essentially double coverage on a receiver with two players. There are two forms. First, there is Inside Out coverage. One defender, say the cornerback has outside leverage on the receiver and the other defender, often a safety has inside leverage, so each guy doesn't have to worry about an inside or outside move, because the other defender has that, they just maintain their leverage so that inside routes and outside routes can both be accounted for. The other method is Hi-Lo Bracket. One defender is pressed and up and will jump short routes while the other is off, taking deeper routes. This allows the short defender to be aggressive and bite while not worrying about the deeper route.
2. 3 Cloud Coverage rolled to the stud WR side- This is a 3 Deep 4 Underneath zone, rolled to the side of the stud WR. This is designed to overload the side of the stud receiver with zone defenders so all the most common routes he can run are covered. The CB will press him at the LOS and funnel him inside. That player will play the flat. The fact that he is up at the line and funnels the receiver inside eliminates the quick out and quick hitch. The slant is accounted for because the OLB plays curl coverage to that side. If the WR runs a fade, comeback, go or post corner the Playside safety plays outside third to that side, so that route is not open. The backside safety plays the deep middle third so the post is gone. The curl route or square in is gone because of that curl defender and a post to square in is probably gone because there is an ILB over the ball in hook zone.
Other common coverages you might see against a stud if lined up wide is Cover 2 man with the CB playing with inside leverage to discourage inside breaking routes and forcing the QB to throw an accurate out route (sideline is an extra defender) and having the deep half safety help for deep outside routes, but the half field safety could have to deal with a vertical threat from an inside receiver, so they probably wouldn't call this against your stud unless you have strong tendencies where the inside receiver on your studs side does NOT run vertical routes. If that is the case, they would also play Quarters. Quarters can result in the CB and S doubling your outside WR if the inside WR to that side (if there is one) does not run a vertical route. When you line up in sets where the stud is the only WR on that side of the center, you will likely see Cov 2 Man or Quarters because they don't have to worry about the slot WR or TE.