From early on, the Nazis "persuaded" Jews to betray other Jews to save themselves, but they never intended to save the Jews who betrayed others. Some of these Jews were the "Jewish Policemen".
Once the Jewish Policemen had given them all the information they wanted (usually about who the rabbi was and addresses of other Jews) they treated those people just like all the other Jews, or worse.
For example, in one Polish town I know of, they rounded up all the Jews in the town square in the summer of 1942 prior to selecting those to transport to Belzec, an extermination camp. Then they asked the Jewish policemen to come forward and hanged them in front of everyone present. This was a common pattern all over Poland.
I realise that many approached in this way were very frightened and must have been desperate to save themselves and their own families. In most cases, they were not saving themselves - only fooling themselves that they would be saved.
So the betrayal of Jewish families and their whereabouts as in the case of Anne Frank was a common method used by the Nazis to find all the Jews in an area and remove them from their homes to a ghetto. In Anne's case, her family were sent to a temporary camp and then to Auschwitz and Bergen Belsen where she, her sister and mother all died.