The viruses in our flu vaccines are supposedly "dead"... infact so dead they don't stimulate the immune response. So the manufacturers add adjuvants to the vaccines to irritate the immune system. It is these adjuvants which do the long term damage.

The smallpox vaccine was a weakened virus and actually caused smallpox and various other nasty things when injected. A very small % of people vaccinated died as a result.
When steroids are given under these circumstances where a weakened but alive virus is in the vaccine, one can get a full blown attack of the disease. (because steroids suppress the immune system).

In a person getting the dead virus however, steroids are still not advised because they will suppress any immune response at all, and NEGATE the vaccine, and hence there will be no immunity at all and it would be all for nothing. (except the irritating adjuvants which will cause inflammation on their own). The only LIVE virus I am aware of is the oral polio vaccine, which comes with a long warning page when it is given to babies.

It is important to understand this. The two situations are vastly different. We do not use weakened live virus in flu vaccines (unless they are accidently contaminated at the site of manufacture).