In 1968, the then circulating Influenza A(H2N2) virus suddenly disappeared and was supplanted by Influenza A(H3N2) virus otherwise known as the Hong Kong flu. Suppose that you were born in the 50s and were at one time infected by the then circulating Influenza A(H2N2) virus, might your immune system still be able recognize that specific variant of the virus if it were ever to return?
Novel research indicated just that: years of influenza exposures plus the yearly injection of the Influenza vaccin, might even protect you from other potential pandemic Influenza subtypes. Subtypes – unlike H2N2 – you’ve never actually been exposed to.
While certainly favorable news, you're not likely to have full immunity, which means you can get seriously ill, but are not likely to die. It might just provide an 'edge' against novel Influenza infection that someone with a more immunologically naive system might not have.
. The study used pseudoviruses bearing various hemagglutinins (the H in Influenza virusses) and they found serum neutralization titers (≥160) in 100% against Influenza A(H2N2), 53% against Influenza A(H9N2), 56% against Influenza A(H3N2v), 11% against Influenza A(H9N2) and 36% against Influenza A(H6N1). None had titers >160 to Influenza A(H7N9) or Influenza A(H7N7). Thirty-six percent to 0% had neutralization titers to various H5N1 strains. Titers to H9, H6, and H5 HA-pseudoviruses correlated with each other, but not with H3N2v, suggesting group-specific cross-neutralization.
Nature is notoriously unpredictable and we never know which Influenza virus will create havoc in the human population next year. It is therefore a sort of comforting thought to know that your yearly vaccination might help you survive that pandemic.
 Wang et al: Serum Samples From Middle-aged Adults Vaccinated Annually with Seasonal Influenza Vaccines Cross-neutralize Some Potential Pandemic Influenza Viruses in Journal of Infectious Diseases - 2015