Pills in tablet form typically consist of the active ingredients mixed with a buffering agent and a caking agent, followed by a coating. Those agents and coating hold the pill together as a tablet, but are not particularly strong and can easily be cut, crushed, or shaved.

The "abuse-resistant" tablets are made by mixing the active ingredients with a polymer, a plastic- or glue-like substance that, when dried, is very hard and slightly malleable. Typically, attempts to crush these tablets simply flatten them out rather than pulverize them. They can still be cut in half, but doing so is more difficult and dangerous than with a standard tablet (you need a very sharp knife/razor to cut them, and you need considerably more effort as well, which increases the risk of injuring yourself while attempting the cut).

Patients who wish to pulverize these pills can still do so using a Dremel or similar power tool, but direct insufflation tends to result in gunking up their nostrils: when the powder mixes with mucous, it turns into a thick goo that clogs the nasal passages. This can be circumvented by cutting the powder with the powder of a crushed over-the-counter medication (typically acetaminophen/paracetamol). At a ≥50% paracetamol ratio, the resulting mucous goo can be avoided entirely.

Patients who wish to inject the substance will also run into the goo problem when trying to dissolve the powder in water or other liquid. The goo is too thick to inject with a typical syringe. I'm almost 100% certain there's a way around this as with insufflation, but I'm not sure what such a method would be. I guarantee you that users who inject already know.

It seems to me that pharmaceutical companies are constantly being surprised by the lengths to which drug addicts will go to get their fix. The only effective way to "combat" drug abuse would be to decriminalize possession and (ab)use of these substances (in the sense that perpetrators will not be regarded as criminals), to start viewing users as sufferers of an illness / mental health problem rather than as criminals, and to make treatment for their addictions readily available without stigma. Slapping addicts with a felony and sending them to prison is the current practice, and it is absolutely ineffective at combating drug abuse. In terms of government funding, I seriously doubt that treatment for addiction will be any more expensive than imprisonment, and it may even be cheaper. Of course, medical providers can do their part by prescribing such addictive substances only as a last resort, and only at the smallest effective dosage.

What do addicts crush/shoot drugs, instead of just eating them?

Higher bioavailability, and faster action. From memory, morphine (as an example) has 100% bioavailability when I'D, but only around 20% orally.

Faster action, more intense high.