Marymac: When my Chester was a senior cat, he displayed the same sort of behavior when his kidneys were failing. The reason: the stools were hard because the moisture in them had been absorbed by the body in an attempt to compensate for the kidney failure. So he was constipated and the stools were difficult to pass, often hanging onto his butt till after he'd left the litter box and then dropping onto the carpet.

Don't know if this is Molly's problem, of course, but it would be wise to get her to the vet (with a recent stool sample if possible), describe her behavior and let the vet run some tests before assuming it's simply a behavior problem... especially since she's 15 years old!