Kidney stones cannot be passed in the stool.
Kidney stones are stones that occur in the pelvis or calyces of the kidneys. When a stone becomes loose or breaks up, it travels down the ureter and reaches the bladder, where the stone may then be passed along the urethra with the urine. The tubes through which kidney stones are expelled are closed, and the stones do not usually move into other tissues.
Stools are formed primarily within the digestive system and are food residues that form in the large intestine after food has been digested and absorbed. Typically, stool is formed and moved within the intestines, which are also in closed tubes.
In summary, stones and stool are in two separate systems, and are formed and moved in relatively closed tubes that generally do not cross over. Stones are not passed out with the stool. If you have kidney stones, it is recommended that you consult a doctor in time and standardize your treatment.