I've accidentally carried knives (generally small ones, a Cold Steel Tuff Lite, a Strider PT clone, a Sage 2, and a BM 530) on planes multiple times in the last few years. I end up having to fly for business travel more some years than others, and it's pretty easy to forget you tossed a knife into a pocket in your backpack at some point. Once I flew both ways without realizing it. Usually I figure out while I'm at my destination, but one time I did find my Benchmade 530 while I was on the plane, sitting right there clipped on the mesh pocket inside the front pocket right next to where the pens go. I was digging for my headphones when I saw it and I freaked out a bit, thinking the 530 would have been hard to explain to the mall security guards manning the x-ray machine if they'd found it, dagger-ey as it looks.
Luckily though, for all the BS security theater of the TSA, they've never once caught the knives I've accidentally carried. They've inspected my backpack for something suspicious they saw on the x-ray, but never on the times that I've had a knife in there.
I suppose my backpack is a challenge, though. I usually have camera gear and electronics crap and chargers and cords and just a mess of metal stuff.
For my part, if you're wondering how I'm brain-damaged enough to carry a knife to the airport, try this. Toss a spare Cold Steel Tuff Lite or Benchmade 530 (small, light, black) into a large pocket filled with black electronics stuff and photo gear, carry then backpack for a few days and then try to find that little bugger again . . .
Now my checked baggage is another matter altogether, they're great at finding knives in there. I had two decent quality knives (~$100 value) disappear from checked luggage before I switched to only packing cheap stuff I wouldn't care about losing.
Instead of packing the WH E10 or Southard I'd usually be carrying, I tend to throw one of these guys in my carry-on (I think I've packed all but the last two on the right of these cheap options on business travel at some point or another):
I've only had one cheap knife stolen, though on that same trip they also stole an iphone (it was in the box, with the charger and everything complete, a company phone, not mine) that was in my checked bag, so I guess they made up for it. That was one of three times I tried filing claims. Let me save you some time: in my experience, it's a total waste of time.
If you do get motivated enough to try to get your stuff back (lolololol) here are some tips from my experiences over the years:
1. You have a short window of time to file, typically the first 24-48 hours (based on the agreement language in your ticket)
2. Even if you didn't get an "inspected by the TSA" slip, file with both the airline and the TSA (the TSA has officially stated that the lack of a slip does not mean they won't hear the complaint)
3. If the value of the item is high (a terrible idea always) also file a police report, the police report may help get your complaint serviced
4. Expect to get nowhere, both will blame each other and claim that yours is the only report, they have monitoring of their employees, and so forth
Why do I always assume it's not the airline baggage handlers, but instead the TSA? I'm sure it's a combination of both, actually, I just believe it more likely to be the TSA based on:
1. They're the only people at the airport with a legal right to open a bag, which means a much reduced level of risk to them in doing it (e.g. baggage handlers are more likely to be caught doing the same thing)
2. I've read multiple ex-TSA employee reports of the rampant theft while they worked there, some bragging about how they were left alone, the only TSA person present, and officially within their rights to open a bag, so it was a no risk theft for them