I certainly like the idea of characters being proactive in finding their own jobs. I don't know about having active bounties by corporations up on shadowboards and the like. It would sort of ruin the element of surprise that most runs depend on if say, "Corp A wants Chemical X" and word gets back to "Corp B" who happens to be synthesizing "Chemical X" (and word WILL get back to them if this is posted in any kind of forum--no matter how shadowy.) "Corp B" will subsequently beef up security and/or move the development site.
The "deadpool" idea is nice. Maybe some street level 'Hooding runs for more altruistic runners. ("Gangers raped my girl/killed my cat/put Fizz-Whiz in my shower head and I've only got

46.32--please somebody make 'em pay!") Might not pay much (if at all) in cold hard nuyen, but might give the players new contacts and the like.
If your players are really motivated and you're feeling quick on your feet with some improv, let them sniff around their contacts and see what happens. If you try to put the ball in their court and/or play off of some of their Qualities, some players might actually discover that their characters have their own agendas that they want to pursue. Especially if it's just one or two of your players, you might even just try to do some "behind the scenes" or downtime roleplaying stuff if you think people would be into that. "It's Saturday night and you're flush from the last run, whadda ya wanna do?" and just go from there. It could be a chance to do just general "maintenance" on their contacts, build new contacts, or just find some kind of unexpected trouble or adventure to get into.