In October 1989, the Communist regime in Hungary followed Poland's lead and agreed to multi-party elections. Setting a trend that would be followed in other former Soviet bloc countries, the Communist Party (Hungarian Socialist Workers' Party) turned itself into a social democratic party, planning to contest the election, in May 1990, against opposition parties.
Communist reformers, led by Karoly Grosz, had taken power in 1988. That led to such liberalizations as the border opening with Austria that I described here.
But attempting to reform the existing system was a half-way course that didn't work in any of the countries in which it was tried, including the Soviet Union under Mikhail Gorbachev. (Unlike the Chinese leaders described in this post, they hadn't read their Machiavelli.)