Can I assume the responsibility for a bond someone else signed for me, so that they will no longer be obligated to the debt.

Sure.


"A surety bond or surety is a promise to pay one party (the obligee) a certain amount if a second party (the principal) fails to meet some obligation, such as fulfilling the terms of a contract. The surety bond protects the obligee against losses resulting from the principal's failure to meet the obligation." Surety bond - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Surety_bond)
You simply get an agreement from the person or entity which is protected by the bond (the obligee) to substitute your bond in place of the other one. If there is a surety involved, you will also need the agreement by the surety.

If this is a bail bond, the person who signed for you, (or, if, a new one is approved, you) would be the principal, the bail bondsman would be an agent of the surety, and the court or the government would be the obligee. The obligation would be that you appear at all scheduled hearings and trial, and of course not try to flee.

Basically what type of bond is it, if the person who issued the bond will agree to it, if this is a bail bond, no they won't normally since if you skip they can't find you to get paid. But if this is a bond for a business, the person who issued the bond will normally just issue a new one with your responsible

... if this is a bail bond, no they won't normally since if you skip they can't find you to get paid. ..

The bonding company (surety) might agree if the obligation is secured by sufficient collateral.