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Potassium is the major cation (positive ion) inside animal cells. Insulin can dramatically alter serum potassium levels by its function of "forcing" cells to take up potassium. Potassium will passively move from the serum into cells, but insulin controls transport mechanisms that move much larger amounts of potassium than the passive means. If insulin isnt available, potassium tends to accumulate in the blood (in serum). Because insulin drives potassium into cells, if its given to an organism with low/low normal serum potassium levels, it can in theory further lower the serum potassium. This can cause some very severe problems, including death. Also, remember in humans that there is an ongoing loss of potassium through the kidneys. This means humans have to take in a certian level of potassium each day or they will become hypokalemic and eventually die. This is especially important in individuals who are on a severely restricted diet, which may be lacking in potassium.
This is yet another reason why people shouldn't mess with insulin.