A former employee in my group at Mega just passed away at 96. He was a mgr when I started in 1979. He was a 35+ year employee. They wanted him to retire. They took away his people, his secretary (back then title) and responsibilities. He wouldn't quit and continued to come in dressed in a suit with a briefcase of magazines. He would shut his door and read magazines for 8 hours. He was ostracized from the rest of the office. He did this until he hit 40 years and then retired. No fanfare. I thought that was incredibly cruel as a new employee, so it wasn't a surprise when the same thing happened to me after 31 years. Except then they had job elimination so I had no choice. If you haven't seen the movie "The Air Up There" it was the screenplay of how they told me - fake meeting, stranger in the meeting, telling me my job was eliminated, a book of details/rights/disclaimers. After my starting experience, I knew it was a matter of time. I was ready and I got a severance, so it was ok. I was one of five in my dept all with over 30+ years.
If they are letting you stay, take it as long as you can. Don't feel guilty don't allow yourself to be shamed by others. You can bet as soon as the time is right they will cut you loose. Good luck