No, you cannot safely ferment vegetables in oil or without water. Fermentation requires an anaerobic (oxygen-free) environment *with* sufficient moisture to allow beneficial bacteria to thrive and produce lactic acid, which preserves the food.
Traditional fermentation relies on lactic acid bacteria (LAB) to convert sugars into lactic acid. This acid lowers the pH of the environment, inhibiting the growth of harmful bacteria and preserving the food. LAB needs water to function.
Oil: Submerging vegetables in oil without any water creates an anaerobic environment, but it doesn't provide the necessary moisture for LAB to thrive. Instead, it creates a perfect environment for *Clostridium botulinum*, the bacteria that produces botulism toxin. Botulism is a serious and potentially fatal illness. While some preparations involve vegetables in oil, these are typically *not* fermented. They are preserved through other methods like pickling with vinegar (which lowers the pH) or by being cooked and then stored in oil to prevent air exposure.
Without Water (Dry Salting): While dry salting *can* be a part of the fermentation process, it's not truly 'without water.' The salt draws moisture out of the vegetables, creating a brine. This brine is essential for the fermentation process. Examples like sauerkraut and kimchi rely on this brine. Preserved lemons are a special case; the high concentration of salt and lemon juice creates an environment too acidic for most harmful bacteria to grow, but it's not a true fermentation in the same way as sauerkraut. The lemons are essentially pickled by the salt and acid.
Therefore, attempting to ferment vegetables solely in oil or without any moisture (beyond what's naturally present and drawn out by salt) is unsafe and can lead to the growth of dangerous bacteria.
Always use a reliable fermentation recipe from a trusted source and follow it precisely. Don't experiment with oil-only or completely dry fermentations without thorough research and understanding of food safety principles. When fermenting, ensure vegetables are fully submerged in brine to prevent mold growth and maintain an anaerobic environment.