Every ending is a new beginning. It's not the end of the world.
On some level anyone over the age of 30 knows this to be true. However it is human nature to go through a grieving period after being let go or rejected regardless of whether it's a relationship or employment.
Many of us identify ourselves by our career which assuages our ego especially if we don't have a well rounded balanced life outside of work.
At some point you realize your future lies ahead of you and not behind you.
Two approaches people tend to have over the age of 50.
1. Find a non-challenging job to work until retirement age with heath insurance. Essentially they just want to coast a few years and retire.
2. Seek out a high powered position or start their own company.
In the case of the first one they may simply post their resume on monster.com, indeed.com, and possibly register with an agency or two in hopes of getting contract work that may lead to full-time employment.
In the case of the second option they're more likely to approach finding a job as if it is their job! They'll take advantage of LinkedIn posting resumes, researching companies, sending resumes to contacts, attending industry networking and professional networking groups via Meetup.com and registering with theladders.com which caters to high salary jobs listings.
Some people have been known to switch careers entirely.
The biggest challenge for anyone who identified them self as their job is avoiding feeling like they are somehow a "loser". People get fired everyday. The issue is many of us may have looked down on them or if we find ourselves in a workshop with others in the same situation we still think somehow we are "better than" them which causes us to feel even more depressed. "I don't (belong) here!"
The reality is no one is their job and failure is a "result" not a "person". We have the option to curl up in a corner and die or fight to climb back to the top. Anger has been a driving force many successes.
What happens to you is less important than what you do with it.
I would also tell them to research and use every resource available.
Our insistence upon "limiting our options" causes us to be depressed.
Ever met anyone who shoots down every suggestion you make?
"If you want something bad enough you will find a way. If you don't you will find an excuse." - Jim Rohn