Generally, charging orders can be issued against
any LLC for a member's debts (all a charging order does is require that the LLC pay any distributions that would go to the member to the creditor instead; a charging order to an LLC for a members debt is similar to an attachment order to an employer for an employees debt.)
In some jurisdictions, though, single member LLCs, unlike multimember LLCs, do not restrict creditors of the member to these kind of actions against the member's financial interest in the LLC, and allow the member's creditors to seek direct payment from the LLC as if it owed the debt.
(Also, in some states, charging orders aren't the exclusive remedy for members debts against multimember LLCs, either, which one reason you need to know the law of the jurisdiction you plan to operate in.)