From my perspective, a Lithops, the situation is dire. You see, my body is not like other plants. My two succulent leaves are not true leaves but a water storage unit, designed by evolution to survive extreme drought. When you overwater me, these storage cells absorb far more water than they were designed to hold. They swell to the point of rupture, and the delicate, specialized tissues inside me that perform photosynthesis are damaged beyond repair. This is called edema. Furthermore, the saturated soil creates an anaerobic environment around my roots, which are incredibly sensitive. Without oxygen, my roots begin to suffocate and rot. This rot is a fast-acting, silent killer; it starts in the roots and will quickly spread up into my main body, turning me to mush from the inside out.
Your first step is to get me out of that wet prison immediately. Gently lift me from the pot, being careful not to damage any parts of me that might still be healthy. Now, you must assess the damage. Gently brush away all the wet soil from my roots and body. Examine me closely. Are my sides splitting open? Is the base soft, mushy, and discolored (yellow, brown, or black)? If the rot is extensive and has reached the main body between my leaves, my chances of survival are very low. However, if the damage seems confined to the roots and my body is still firm, even if overly swollen, there is hope.
Using a sterile, sharp knife or scissors, you must carefully cut away any rotten roots and tissue. This feels drastic, but it is necessary to stop the spread of decay. Remove all roots that are not firm and white or light tan. You may be left with very little root structure, and that is okay. Once the rot is removed, I need a critical period of dryness. Place me in a warm, dry, and well-ventilated area out of direct, harsh sunlight. Leave me bare-rooted like this for several days to a week, or even longer. This allows my wounds to callous over completely, forming a hard seal that will prevent new fungal or bacterial infections when I am repotted.
After I have fully calloused, it is time to give me a new home. The pot must have excellent drainage holes. My new soil is my lifeline; it must be a very gritty, fast-draining mix specifically for mesembs, often containing a high percentage of perlite, pumice, or coarse sand. Do not use standard potting soil. Gently place me on top of the dry soil mix and barely nestle my remaining roots in. Do not water me. The temptation will be great, but you must resist. My remaining tissue still holds plenty of water to sustain me.
This is the hardest part for you, but the most critical for me. You must not water me until I show definite signs of needing it. This could be many weeks or even months. The sign you are waiting for is the natural wrinkling of my sides, not on the top surface. The old, overwatered body will eventually be consumed by a new set of leaves growing from my center. Only when the old leaves have completely withered into a papery shell and the new plant is visibly wrinkled should you consider a very small, careful drink of water. My entire survival depends on you mimicking the harsh, dry conditions I am built for.