You can use an Assignment to opt out of the rights and obligations of a contract in place of someone else as long as the original contract doesn't prohibit assignment and assumption of obligations. It's a good idea to check the original contract terms to ensure you aren't still liable for the terms of the original contract after assigning it to a new party.
You may want to consider getting the second party of the original contract to sign a Release/Waiver Agreement to absolve yourself from any liability from the contract.
It's also possible to transfer the benefits of an income stream to an assignee using an assignment agreement.
For instance, let's say you upload videos on social media that garner money, and it turns out you may have used parts of someone else's footage or material. To settle a possible copyright dispute, you could use an Assignment to transfer part of the income stream you receive from the video with the other party's material to the other party for a period of time.
Sometimes an Assignment can technically be used to transfer rights to personal or intellectual property, but, in most cases, it's best practice to use more specific forms like a Bill of Sale, a Trademark Assignment, or an Assignment of Trade Name.