File under "well, it's worth considering even if it isn't fully thought through as yet."
Unemployment is usually between 5% to 10%. That means that for every one person who is unemployed, there are 9 to 19 people who are employed. Why not a mentor program that gives each unemployed person access to the 9 to 19 who are employed? It could be both value and prod to the unemployed and a form of service tax on the employed.
There are a lot of things that could be done with this model, but essentially you'd raise the probability that someone out of the labor market still had connections to it. The employed mentors (EMs?) could offer interview tips, share job leads, suggest training programs, give feedback about where to apply, etc. Mentor teams could track their numbers against national averages, looking at numbers like time to get their apprentice into a job, ratio of pay in last job to next job, etc.
Particularly for the long-term unemployed, it is easy to become disconnected from prevailing norms, trends, and even the hope that comes from talking to people who show an interest. A program like this might help.