Encouraging parents who refuses to save

As per the post, how do you deal with parents who refuses to save?

For context, my parents are divorced and I give monthly allowance to both my parents. Thankfully, my dad has started saving up for the future and has been doing it for the past few years. My mum, on the other hand, does not have such a habit. Recently, I told her that she should try to save a portion of the money I give to her. She said that she can depend on us (My sister and I). I told her that medical bills will be expensive and she said that insurance and again, children will be able to cover all that. She keeps saying that we should not be too thrifty and enjoy the money as after we die, it will go nowhere.

My worry is her finances in the future. How do I encourage her to start saving up? I was thinking of reducing her monthly allowance and saving on her behalf (with her knowledge). Shes in her mid-50s btw.