The US government did that as well back in the 80s when it converted from CSRS to FERS. The unfunded obligation of the old system is something like $800 billion and won't be settled until 2090. The new system is a mix of SS, defined benefit, and defined contribution and is expected to stay solvent indefinitely. New federal employees hired after 2013 got screwed, however, as they upped their contribution rate to cover the massive problem CSRS caused.