does this job exists ?

I was in a senior home for almost 2 months.  During that time I tried to do every activity: chorus, day trips, evening concerts, minor activities, game days, etc. We had a director of activities: four of us came to play games, cards, a different five came for Trivia.  No one wanted to go to the Triple A  baseball games for free. But it is the people who were duds! They were board, almost lifeless, ALWAYS pushing walkers to get to the dining room, never interested in doing anything fun, waiting instead in their apartments, waiting to die.  Oh they had energy for the "free" health checks in the commons area, or to run down to the "beauty parlor" to make their white hair grey or blue???  Every day after dinner, about 5 pm, the whole place turned into a morgue, when I took my puppy out for walks every two hours until midnight, there was may be 2 people out side walking like me.  I even goaded the director to instigate visitations to units we NEVER even saw at meals (they took delivered meals)--I got stone walled.  I had to break my 1 year lease, because for $2500 a month they were warehousing bodies that had given up.  You idea of this job doesn't seem to be in demand, it's the lifeless, motionless, unwilling bags of bones who refuse to live, choosing to just stay to themselves.  250-300 unsocial HERMITS!  It was me that went to up-lift the very nice ladies that came in to do hospice:  I figured they had the worst jobs in the world: 12 hour shifts watching some one die week in and week out, I just wanted to get them to vent, to release their inner pressures of intimately knowing people, and horribly seeing their death a few weeks later--got to be hard on them. 

It is called volunteering. 

Not as a paid job, no.  Many people do that sort of thing as a volunteer.

Sounds more like a companion job, I guess it is if you ask around. Maybe some hospitals have it?

The word is BORED not BOARDED.

I entertained the seniors at a nursing home with a puppet show once. But I did it for free. If you mean a job to do it for money, I don't know.

Yes.  It's called "companion." 

I think the residents of the Senior Home would ask you to leave after a few minutes.

There are many residential homes who need people as you describe - they are usually called 'befrienders' but those jobs do not pay a salary - you might not even be given your bus fare.  Don't embark on doing such a thing unless your heart is in it totally and that you realise your reward will be just a good feeling because you will have cheered someone up.  

Such roles have been needed for decades. I was asked (about 60 years ago) to take up such a role by seeing a lady in a mental hospital who NEVER had visitors. She was delighted when I turned up on Sunday afternoons. It's rewarding but, sometimes, hard going.

that might be a volunteer job