Are there some products that cannot be insured for product liability?

The quick answer is yes and no. (I know. Useful, right?)

Let's flesh this out a bit.

Businesses are held accountable for their products. If a customer purchases a product and a defect in it causes either bodily injury, sickness, or property damage, the manufacturer or the retailer may be held liable.

In insurance terminology, a defect means that something was either missing or something that should have been included was left out. This generally applies to a design or manufacturing defects (say, a kitchen appliance with a part of a few screws missing) but it can also apply to marketing defects (missing or incorrect labeling or instructions).

Most product liability insurance policies are pretty complicated, and there is currently no cross-industry standard. But insurance companies will exclude products (or products containing certain ingredients) in order to limit their risk exposure, so there are some risky products that most companies won't insure.

Outside of those that are blatantly illegal, there are, for example, products in certain "high-risk" industries (pharmaceuticals, dietary supplements, "nutraceuticals", and so on) are typically excluded from typical product liability policies. But in some circumstances, even these products can be negotiated back in.

I recently had a client, for instance, who wanted to buy some insurance for his herbal supplement manufacturing business. When negotiating with the underwriters, it became clear that there were several ingredients that would exclude a product from coverage if it contained them. These weren't just illicit or inherently dangerous ingredients, but also included several common ones like creatine and St. John's wort. As mentioned above, however, these exclusions are not always set in stone. In this case, I could use my client's experience and good track record to have those exclusions waived.

In summary, insurers are reluctant to insure medicines and other products meant for human consumption. Beyond those, however, there is little broad-based consensus about what products should be excluded.