An elderly person can go a week or even 2 weeks without a bowel movement which is normal depending on the elderly persons diet.
There's really no set amount of times or length of time that a person can go without pooping.
Depending on your diet it can be normal to go a few weeks without needing to poop as the less fiber you eat the less you need to poop.
As long as the elderly person is pooping at least every few weeks then they likely are okay but any longer than a few weeks between needing to poop or being able to poop then the elderly person may be constipated.
Constipation is more common in older and elderly people than younger people.
Also as you get older your bowel habits usually change which is also normal.
The cause of an elderly person losing control of their bowels can be nerve damage to their bowel muscles, weakened bowel muscles and even Gastrointestinal Diseases.
Not every elderly person does lose bowel control but some do.
Also some elderly patients such as those with dementia or other brain diseases may lose bowel control because their brain helps control the nerves to their bowels as well as their bladder.
Bowel incontinence and urinary incontinence is not a normal part of aging because not every person who gets old loses bladder or bowel control.
There have been people who lived beyond 100 years old and never had bladder or bowel incontinence or even dementia.
It's just that some people have those issues and some do not.
Also some elderly people may have control of their bladder or bowels but need reminded to go to the toilet and or need help going to the toilet.
If the elderly person is bowel or bladder incontinent then they should wear adult diapers and have them changed often or change them themselves if they can.