I see here two different situations which I will try to answer:
1. Your family comes to Germany while you are still in the asylum process
Your cases will all be examined together as a family. If one of the following types of residency status is then given, all members of the family will receive that status:
If, however, a status of deportation ban (Abschiebungsverbot) is given, it is not necessarily given to all members of the family. This means one member of the family could receive a deportation ban while another is obliged to leave the country.
Here is more about this from BAMF:
2. Your family comes to Germany after your case has been decided upon
If you receive a protection status (refugee/subsidiary protection/deportation ban) then if certain requirements are fulfilled, your family can receive a visa to come to Germany. When they get here, they will receive a residence permit as your family members (this is a different kind of status to yours).
They have the option when in Germany to make their own applications for asylum. You would need to discuss the advantages and disadvantages of doing this beforehand.
If your case for protection is turned down and you receive a Duldung or deportation order, then you do not have the right to bring your family to Germany.
Here is more information:
Let us know if you have further questions about this.