thank you for sharing your question with us.
I am not an expert on this topic, but as far as I found out, the Sozialamt does not have to take over your debts in any case. They can do it if this would prevent a distress (like loosing your appartment for example). I recommend you open a new bank account and make an installment plan with the Inkasso office. If you need help with this, you could contact a debt counseler.
I hope my answers were useful for you and I'll be very pleased if you contact me again with further questions. I'm a member of the MBEON-staff and I‘ll be glad to guide you over a longer period of time. Mbeon is an online consultancy for migrants via the mbeon-app, which you can install on your smartphone for free. Download it via App Store or Google Play Store. You'll find me In the mbeon-app under my name „Euskirchen, Frau Schaefer“ and get confidential one-to-one advice in a safe virtual room where nobody can wiretap messages. Further information: www.mbeon.de