You need to consider the overall team shape and roles and duties, because changing one and not considering the others will cause problems elsewhere. It depends what formation you're playing.
I'm playing a 4-3-3, and I had this problem a lot when I first started so I put my fullbacks to FB-S, player instructions to stay on feet (the last thing you want them to do is go in for a sliding tackle, miss, and then leave the entire wing area open for them to dribble into and pick out a perfect cross). No man marking, just zonal, because you will have the same problem if the opposition wide men switch.
The full backs should stay back and do a better job of picking out those flank clearances / passes. If you're still struggling try playing a more CB type player there rather than a complete wing back (Balanta for example, will just vacuum up anything knocked down his flank). The problem now is that if you play wide forwards who don't take advantage of the wings, like an advanced playmaker or a raumdeuter for example, that you have no wide play. I have a raumdeuter on the left and a winger-Attk on the right. In my flat midfield 3 i have a roaming playmaker, advanced playmaker and a cm-d. I like the AM-C to play through the middle, and he has a PPM for it, so no point in asking him to help out wide, so I ask my roaming playmaker to run wide with the ball. He runs out with it, the raumdeuter looks for the space created by my F9 and my right winger does his thing on the opposite side. If this leaves you feeling a bit skinny in midfield, push your defense higher up, or consider changing one of your FBs to an inverted wing back so he steps in to the centre of midfield. Doing this will expose your flank again but it's preferable to having the opposition pass straight through the centre of your midfield.
EDIT: If things are really bad (like, Brazil vs Germany bad) and you're wide defenders are getting dicked all over by the opposition wide attackers try playing limited full backs. I wouldn't do this because it doesnt suit my attacking style and leaves too many areas of my team unsupported but it might be worth a try, so long as you compensate with changes to other roles and duties.