You've found a solution that could help them. You've read information about fall prevention. And yet, the answer is always the same: "I don't need it."
The real problem is often not the protection itself
Protection can be interpreted as a loss of independence, a sign of aging, or confirmation of frailty. That's why the conversation is usually more emotional than rational.
Talk about peace of mind, not incapacitation
Instead of saying, "You need it because you might fall," say, "It would help me feel more at ease when I'm not with you."
Involve them in the decision
People are much more accepting of things they feel they have chosen. Let them choose the color, the model, when to use it.
Appearance matters more than it seems
Nobody wants to wear something that reminds them they are getting older. Modern designs have evolved precisely for that reason.
You may also be interested in: How to talk to your elderly parents about their safety without offending them | My father won't accept help: how to protect him without conflict | Do your parents feel unsafe when walking?
If you are looking for comfortable and discreet protection for everyday use, you can learn about SafeSeniors here.