I'm wondering if what you saw in your urine that looked like part of a pill was actually a small bladder stone, or even a smaller kidney stone that made its way thru the ureter from the kidney into the bladder & out thru the urethra? Often there's considerable pain from kidney stones, but apparently sometimes they can pass thru without causing much of a problem. I would ask your Dr. and/or a Urologist about this...
No, this is not possible. The ileocecal valve separates the small intestine from the lower intestine (colon). Water & liquid wastes are separated from the intestine & processed thru the kidneys - the resultant fluid waste is urine, the of course. So these are two separate systems & it’s not possible for part of an undigested pill to make its way into the urinary system. However, there are cases where a fistula exists & fecal contents can enter the bladder, obviously a very serious situation that would require a surgical repair. I’m wondering what you saw in your urine that caused you to ask this question? If there IS any possibility of intestinal contents entering the bladder, you should get to a Dr right away, but I think that’s a rather remote possibility. It does happen but is pretty rare...