There is a difference between an owner and a signer.
An owner is the legal owner of the funds. A signer has access to withdraw the funds. In most cases, when a new personal account is opened the name is added as an owner&signer. However, that is not always the case.
A person could be an owner, but not a signer, in a custodial arrangement. For example, a minor child may be an owner only on their account with a custodial parent listed as a signer. The minor could not withdraw from the account.
A person could be a signer, but not an owner, in a business or estate/trust account. The business or estate would be the owner with individuals listed as signers only. The business employees do not own the funds, they are only allowed to withdraw and disburse the funds on behalf of the company.
The creditor can only garnish/withhold funds that are owned by the indebted. If the second person on the account is only a signer, those funds cannot be withheld as part of a judgment against the second person (they don't own those funds).
However, simply titling the second person as a signer only is not sufficient. If you share access with the second person and allow them to spend the money for their own benefit, they are no longer just a signer. They have become an owner because you are sharing your funds with them. Think of the business relationship as an example. The employee is a signer so they can withdraw funds and pay business expenses, like the electric bill. If the employee withdrew funds and bought herself a new dress, she is stealing because she does not own those funds.
If the second person on the account buys things for themselves, or transfers some of the money into their own account, they are demonstrating that more than a signer-only relationship exists. A true signer-only relationship is where the individual can only withdraw funds on the owner's behalf. For example, the owner is out of town and needs a bill paid, the signer can write a check and pay the bill for the owner.
A limited power of attorney may be worth looking into. With a limited POA, the owner can define the scope and expiration of the power of attorney. With this arrangement, the second person becomes an executor of the owner under certain circumstances. For example, you could write a power of attorney that states something like:
John Smith is hereby granted the limited power to withdraw funds from account 1234, on deposit at Anytown Bank, for the purpose of paying debts and obligations and otherwise maintain my estate in the event of my incapacitation or inability to attend to my own affairs. This Power of Attorney shall expire on it's fifth anniversary unless renewed.
If the person you have granted the power of attorney abuses their access, you could sue them and you would only have to demonstrate that they overstepped the scope of their power.