Several members of my family were members of the KPD in East Prussia before the Nazi takeover. Afterwards, almost all of them were killed in concentration camps. I'm wondering if this fate was common amongst members of the KPD.
Yes, this was a fairly common fate. To give some numbers, in November of 1932 there were 330.000 KPD members. During the 3rd Reich, according to Bernhard Bayerlein, 50 000 KPD members were killed, and a further 150.000 arrested, many of them subsequently sent to concentration camps. Keep in mind, however, that, while members were savagely persecuted, many KPD voters were ‘accepted’ in the Nazi Gleichschaltung process, especially many of the newer voters who where won over by the pan-germanic KPD propaganda of newer elections, in a somewhat bizarre attempt to be more nationalist than the National Socialists.