I was surprised when my new boss said I was not a good fit anymore but wanted me to train my replacement and if "appropriate" I would be given a week's severance if the "transition" went well at the end of the two weeks. I never got any bad warnings, and in fact in January, my other boss gave me a $2 an hour raise. Also the new boss, who just happens to be my other boss's father, is insisting that I go to the same employment agency he used to get my replacement, trying to push it off as doing a good deed for me! I think it's because he may be concerned about paying unemployment. I am in my 60's , my replacement is 39. Should I go to the agency? I think it's fishy. My gut says no because what if the agency sends me to a much lower paying job or farther away than I want to travel to work, and turn it down, I won't be eligible for unemployment. I need some feedback.
Being in your 60's it's going to be difficult to find employment. However I would not trust the bosses, they just want to get rid of you.
If at all possible job hunt on your own and leave as soon as you can. If you can find employment before training a replacement, just leave. An offer of a weeks severance contingent on them being happy is not much.
Meanwhile work conscientiously as normal.