Detoxification is one of the primary functions of the liver. When you ingest something, if it is absorbed, it enters the portal vein which delivers the blood directly to the liver. There, the liver metabolizes, "detoxifies", excretes, synthesizes, and stores.
What needs to be stored
The liver stores excess glucose in the form of glycogen, fat-soluable vitamins A, D, K, iron used for the synthesis of red blood cells, copper (used as an integral part of enzymes), fat, B12, and some other substances. (This is why eating polar bear liver results in hypervitaminosis A.) It does not store toxins.
How the liver "detoxifies"
The liver has a staggering number of metabolic pathways involving a series of enzymatic reactions that neutralize and solubilize toxins for excretion by the liver or kidney. It should be noted that some of the same enzymes are used to render "pro-drugs" into active drugs, and that delivery of absorbed molecules directly to the liver (where they may be converted or removed, called "first pass" metabolism) is the reason that some drugs simply are less effective or ineffective if taken by mouth. (The gut also is responsible for some metabolism.) This is so much a feature of the liver that first-pass metabolism of medications must be taken into consideration to determine the right dose of a drug.
Generally lipid soluble toxins are first made water soluble by any of a group of enzymes called the CYPs, e.g. cytochrome P450. Each of these enzymes has the potential to alter very many different toxins. Liver enzymes then add another water soluble molecule (called conjugation) to the toxin which renders it less toxic and water-soluable enough to be transported for excretion by the liver (with bile, which is excreted into the intestines and carried out of the GI Tract) or the kidneys (in urine).
Toxins can kill the host, injure a specific tissue (for example, an overdose of acetaminophen can cause enough liver damage to shut down detoxification leading to death), act as carcinogens altering DNA, be metabolized and excreted, sometimes be stored in adipose tissue (fat), or take other routes through the body. I personally know of no toxin (nor could I find one) that can bypass these things and be stored in the liver.
There are toxins that damage the liver: alcohol for example. Yet that doesn't get stored in even a damaged liver.
Clearly there are toxins everywhere that we don't even know about, but if drugs and toxins* studied are metabolized and excreted by the liver (or follow other routes), it stands to reason that the ones we don't know about are probably being handled similarly.
*Disclaimer: Heavy metals are handled differently. Also, this answer doesn't deal with concentration of toxins in other tissues, e.g. fat. (Some toxins are stored in fat cells, and become mobilized again on weight loss.)
FUNCTIONS OF THE LIVER
The Physiology of the Liver
Effects of yo-yo diet, caloric restriction, and olestra on tissue distribution of hexachlorobenzene