The term "empty nest elderly" may not be easily understood by everyone. So it is best to enclose it in quotes and describe what it means early in your essay so your readers can follow you. Because of this, I need to change first the paragraph a bit to make it clearer. 

Old people

With the development of society, the older generation has witnessed the country's phenomenal (rapid) growth.  More children are are finding work further away from their parents hence they need to move out of their parents home and stay closer to their work or place of study.  and they are also becoming This is creating a situation called "empty nest elderly" where children have left home or left the "nest" so to speak. generally. It seems that society is flourishing but they are been forgiving are our elderly being forgotten ? 

As we know, it is necessary for the old to live with their partners or a family nurse in order to prevent them from appearing having an emergency without anyone around to help.

But to tell you the truth, this social phenomena makes me feel embarrassed. Because it reminds me of my grandpa. My grandfather passed away when I was in junior high school. But I can still remember the situation at that time. I have two aunts and two uncles, which means that there were at least five children for my grandpa who could have taken care of him. But my grandpa died alone at home without any help from his children. At last, it was one of his friends who found him dying when planning to have a spare conversation with him. However, I don't wanna express any condemnation on anyone. Because I know that every family has their own difficulties(or problems) unconvenience at that moment.

Maybe I am so indifferent that I feel it is normal. And empty nest elderly are not supposed to be sympathetic. I support agree (or understand) we should take different actions for different old elderly people, not only mency (not sure what you mean by "mency"). Some old elderly (old is okay but elderly or senior sounds nicer) people still want to pursue a creative lifestyle with positive attitude. It is also possible for the large majority of elderly (or seniors) to face their lonely and quiet later years. 

I think the old should learn to accept ageing and abrupt death, just like the young are learning to adapt themselves to indifferent changing society. Comparing with Instead of expecting the younger generation to spend time on looking after the old, I suggest elderly's creating a colorful later years retirement by themselves. No matter how crazy or quiet it is, it belongs to the old thier own themselves.  

As for health issue, i believe it will be nice to set up a punch-clock system to ensure every old people can go out for normal activity.

It may seem s that I am still too naive. But what I wanna say is that ageing is exactly a lonely and disturbing thing. But I hope the elderly can have a positive attitude when they are on the road. I wish every old person is able to go to the other magical place with pleasure and not full disappointment.