The shrinking of the public sector will bring a new economic prospect for blacks. They have usually occupied public sector jobs at a higher rate than whites so this will encourage them to find work in the private sector. This will be good for them because it is better to work in privaate sector.
Without looking a statistics, I would guess that it is easier for an African-American to find a public sector job than a private sector one. With programs like InRoads, there are internship possibilities at private companies that can lead to future jobs. With so much competition for jobs, it's not going to be easy to find private sector jobs just because the public sector is shrinking.
I believe the shrinking of the Public-Sector will find people of all races out of work and seeking jobs in the private sector and the private sector hires people based on ability and experience, so I see no problems for African-Americans to find new job opportunities if they have the relevant skills and experiences needed.
Since shrinking the public sector actually results in people losing jobs, I don't see how it could improve the economic prospects of African Americans - or anyone else. The only possible gain of shedding public sector jobs would be a small savings on the part of tax payers, but not enough to make any real difference in terms of economic prospects.
Black Americans make up a disproportionately high amount of public sector jobs. This is largely due to affirmative action and other minority hiring programs that work specifically to hire and retain black workers. Black workers who have become accustomed and reliant on these special programs are unlikely to be competitive in the private sector, as these are not as prevalent as with governemnt employment.