I've had a female lay eggs without ever mating, but flipping on her back sounds to me like a weird way to relieve the pain.I believe female leopard geckos can sometimes ovulate even if they don't mate, though I could be wrong.
Inpherno says that the round mass was brown inside so it doesn't seem a follicle, but... A friend of mine had to put down a knob-tail gecko female that wasn't thriving after two surgeries to take out some eggs that she wouldn't pass. When they performed the necropsy, they found another pair of eggs, that were brownish-black! She was diagnosed with herpes... Weird.
Inpherno, if you can provide some pics of the tank, gecko, and the thing she excreted, we may be able to tell you something else.
If you get any other "stool" store it in the fridge until you can take it to the vet. Good luck.
