It varies widely.

The Czech communist party is both the most successful and the only one that has not really substantially changed, its leaders are still essentially apologists for the Czech communist regime. For a long time it was quarantined by post Czech governments, but that quarantine was controversially recently ended.

The German Socialist Unity Party was taken over by reformers towards the end of the GDP and tried to reposition itself as a social democratic party but without much success throughout the 90s, largely because Germany already had a big, successful social democratic party. In the 2000s it had some minor successes and eventually allied with a West German left group without a communist heritage to form Die Linke which is a modestly successful party with representation in the Reichstag and sharing government of some Lande.

The Polish communist party, similar to the German party, was also taken over by reformists before communist role collapsed, also reformed itself into a Social Democratic party with more immediate success in the 90s, and in the early 2000s dominated Polish politics. Its leader, Alexander Kwasniewski, was President of Poland from 1995 to 2005 (he had previously been a junior politburo member) although as President he distanced himself from his party and moved to the centre. The party suffered a major collapse in support in the late 00s and renamed itself several times, it now survives as a minor component of a pan-left coalition of parties but like most of the Polish left it has very little political support:

The Hungarian Socialist Workers Party transformed itself into the Hungarian Socialist Party, a social democratic party, and for a long time was one of the two major Hungarian parties, controlling the government several times, but recently it has fallen in support as part of the general collapse of the Hungarian left, although it is in healthier shape than its Polish counterpart.

The Romanian Communist Party dissolved and wasnt reformed. Although its members continued to retain positions of power, they werent able to hold the party together, probably because of the uniquely violent nature of the fall of communism in Romania.

The Bulgarian Communist Party, again, already in the hands of reformers, transformed itself into the Bulgarian Socialist Party, and managed to win the first reasonably free elections after the fall of communism. It has always been either the government or the opposition.

So, overall, the goal of communist parties towards the fall of communism was to reconstitute themselves into western style social democratic parties and win elections. Some were more successful than others. The Romanian Communist Party obviously failed the hardest, the Polish party initially appeared successful but long term was unable to survive, the East German Party initially appeared to have vanished into irrelevance but managed a partial comeback, while the Bulgarian and Hungarian Parties were the most successful and are still major political forces. The Czech Party is a bit of an exception in that it never really aspired to be social democratic and doesnt really think there was anything wrong with the Czech communist state - all the other parties, even the relatively hardline ones like Die Linke, are critical of the Soviet satellite era.