What happens when a liver tumor from colon cancer no longer responds to any treatment and is growing?

If it isn't responding to treatment, the outcome is grim. It will most likely spread to more areas of the body and the person will inevitable not survive much longer.

Very sad.

When cancer stops responding to treatment than the disease will continue to grow indefinitely and spred throughout the body.
There is usually palliative treatment offered to keep the patient comfortable and it is even possible to try Clinical Trials in an effort to bring the disease under control. In some cases efforts can be made to control the disease rather than try and 'cure' it . . and the patient can live with his cancer.

Best thing to do if you know someone in this situation and they want to continue in treatment is to ask about Clinical Trials . . there are many new drugs available for cancer patients, the trials are usually sponsored so there is no cost involved. Clinical Trials will give the patient access to the newest available treatments although it is a chance.

By "any treatment" I assume that you mean any conventional treatment. Most tumors contain a small percentage, approximately 2%, of MDR (multiple drug-resistant) cells. Chemo is not effective against these cells. After the first round of chemo, if the chemo is effective, all of the cells that are not MDR, are destroyed. Since this accounts for the vast majority of the tumor mass, the tumor appears to be effectively destroyed. However, the MDR cells remain and start to multiply. If the cancer reoccurs due to MDR cells, the new tumor is likely to be entirely MDR. The next time chemo is used, none of the cells will be destroyed because they are all MDR. This is why giving chemo after a cancer reoccurs often fails to have any effect. Only alternative health care has treatments that have been shown to be effective against MDR cells. These include Paw Paw and Graviola. Have you read this Paw Paw page: