Combine water, salt, lime juice, chiles de arbol, and Guajillo chiles in a large pot and bring to a boil.
Once ingredients are boiling, remove from heat and let the brine cool.
Combine the cabbage and brine in a large, nonreactive container.
Cover the cabbage with piece of cheesecloth or a clean kitchen towel, then weigh the cabbage and cloth down with a plate, pressing the plate down so that the cabbage is completely submerged.
Cover the container loosely with plastic wrap and set in a cool place for two weeks (it can be no warmer than 70 - 75 degree, otherwise no beneficial bacteria can begin to thrive.)
After two weeks, drain the cabbage, reserving the brining liquid; the cabbage should have a pleasant sour/salty flavor and although its green color will have paled, it should still be crunchy.
Strain the brining liquid into a pot, then cover and refrigerate the cabbage.
Bring the brining liquid to a boil, remove from the heat and let cool to room temperature, then chill.
Pour enough of the cold brine over the sauerkraut to cover it completely, discard the extra brine.
Cover and store in the refrigerator for up to three weeks.