By design, yes. In practice, things don't always go as planned.

I have had two problems with fragmenting bullets in the past (specifically CT Ballistic Silvertips and Hornady V-max's), always at short ranges.

1) At close range, these can over-expand on impact, causing a large entry wound and no exit. It's like the up-splash after you do a cannonball in the pool, that "ka-doosh" splash that raises straight up in the air. Fragmenting bullets at extremely high velocities can cause "rebound wounds", basically blowing back out the entry wound. I had this happen on a whitetail deer with a .30-06 and Winchester Ballistic Silvertips, then also on two coyotes with a .223rem and V-max's, all of them under 30yrds.

2) Also at close range, if a fragmenting bullet DOES exit, it's usually a bloody mess. While a controlled expansion bullet might leave a golfball sized exit, a frag bullet might leave a softball sized exit. Or, if the bullet fragments and the pieces exit, you're left with multiple quarter sized exit holes. On yotes under 40yrds, I've had V-max's and CT BST's produce terrible exit wounds.

So moral of the story, I feel like I got penalized for doing a good job. The closer I called a coyote, the more I was at risk of doing excessive pelt damage. For me, fragmenting bullets are an all or nothing. Either they work great, and produce VERY little pelt damage, or they unintentionally exit, and they do a ton of damage.

Obviously they work. They're just not my preference. Your mileage may vary.