I'd be interested to hear if anyone here has a counter example. I certainly don't. I don't seem to have every got anything useful out of it.
I can give you three examples from my own experience.
1. My LinkedIn connections (former colleagues, mostly) have contacted me to see if my employer is hiring or if I can submit their resume for a job posting. I have helped many folks secure jobs this way.
2. I have also been approached by people in my LinkedIn network, asking if I wanted to come work with them. I have gotten several jobs that way. (When I wasn't even looking for a job.)
3. The reverse of #2 -- When looking for people to join my team, I go through my LinkedIn network and ask folks if they might be interested in working on a new project.
The best way to find a rewarding job is via networking (i.e. word of mouth), and LinkedIn makes networking very easy.
The best time to recruit someone (former colleague) is when they are not looking.