Many foundations give away bursaries to especially talented and successful students of PhD students.
Most of the time, bursaries, which are similar to the BAföG maximum, cover living costs. Some foundations grant book allowances. In addition to financial support, the foundations offer their bursary holders participation in seminars and network meetings.
The foundations have highly different support criteria—the range goes from being a member in a certain church to being closely connected to a political party or a trade union. Some foundation especially support talented young people with a migration background or from financially weak families.
Get an overview of the foundation through the websites "Stipendienlotse" of the Federal Office for Education and Research, mystipendium.de or „Studienförderung“ of the Association of German Foundations. There you can look for special support opportunities of your own university.