I suspect that the law on this point varies from state to state. In my jurisdiction, a creditor cannot become a "substituted partner," and I suspect the result is the same for members of an LLC. The creditor gets a "charging order" entitling him to whatever distributions are made, but I am not aware of any mechanism for forcing such distributions to occur. Consequently, a charging order is not an especially effective collection tool in this state.
Yes, there is state variability, but there also is federal bankruptcy law which often trumps state law. For example, most states have adopted the Uniform Limited Partnership Act. The Uniform Limited Partnership Act provides that a creditor cannot take assets of a limited partnership to satisfy the debt of a limited partner. Basically, the partnership isn't liable for the debts of the individual limited partners. It also provides that a creditor of a limited partner can "charge" that partner's interest to pay a judgment, and that the creditor will be treated like an assignee of the partnership interest.
This does not mean that a creditor cannot take a limited partner's interest in the partnership to satisfy that partner's debt.
Some states do, however, limit the ability of the creditor to "take" the partner's interest. This is where your charging order comes in. The creditor will get an order of the court requiring any distributions to the partner be paid to the creditor. The creditor just sits and waits or settles with the debtor or other partners.
However, the trend (at least it was a trend a couple of years ago when I last checked) is to allow the liquidation of partner's interest in a partnership if the creditor's judgment cannot be satisfied by the charging order. Bankruptcy courts are especially likely to allow the liquidation. Because of this trend and the fact you can't be sure where you will get sued and what state's law applies, there is always the risk that a creditor or bankruptcy trustee will successfully obtain ownership of the limited partner's interest. My experience is that determined bankruptcy trustees do not let go of valuable assets and one way or another, manage a recovery for creditors.
The practical problem still remains, however. Even if the creditor gets ownership of the limited partnership interest, it is going to be hard to force a distribution. Nevertheless, a determined creditor or trustee will likely be able to squeeze something out of the partnership interest.
It is worse for the debtor if the debtor is both the general partner and a limited partner. Or even just a general partner. Say dad sets up a limited partnership. Dad is the GP and is a LP along with his kids. Dad ends up in financial trouble and files bankruptcy. As trustee, I would step into his shoes as GP and force a distribution to the LPS.
In any entity, if the debtor has controlling interest, a bankruptcy trustee will likely be able to exercise that controlling interest and force a sale of the controlling interest, or the entity itself or its assets.