How do I say 'unwanted pooping?'

You could use the word incontinence defined by the Collins dictionary as

the inability to prevent urine or faeces coming out of your body.

• Incontinence is not just a condition of old age.

The Merriam-Webster dictionary describes incontinence as

inability of the body to control the evacuative functions of urination or defecation partial or complete loss of bladder or bowel control

• fecal incontinence
• urinary incontinence — see also stress incontinence, urge incontinence

As populations continue to age, more and more elderly people need to rely on adult diapers or incontinence pads. Diapers is US English and nappies is UK English.