What would you say to your manager who asked you to train your replacement after you've been given a layoff notice?
As long as you’re on the payroll, you are obligated to train the new people. If you aren’t willing to do this, and I understand why you wouldn’t, you should resign immediately.
I would also ask the supervisor why you’re being laid off if he/she values your skills enough to train your replacement, perhaps there is another position in the division or company where you could transfer.
This happened to me when I asked to be transferred to a different division that had another product line rather than be laid off. Another time, I asked to be transferred to a different city where the company had an office. I kept my salary tenure and benefits. It was easy for me since I was single and rented an apartment and the cost of living was lower at the new location, to boot.