Your assets are generally protected, but you need to make sure you keep your business and personal finances completely separate. You can also be liable if you do something illegal, unethical, or irresponsible. If you have a large business, it doesn't hurt to have your home put in your spouse's name, if you have one. A lot of professionals do that just in case something happens. Anyone can sue you personally if they choose to - whether or not they will be successful is a different story.
It is always a good idea to have business insurance. It seems unlikely that you would be sued for selling products on behalf of someone else. But the more layers of protection you put in place, the easier you can sleep.
Protection from personal liability is a major benefit of forming and conducting business as a Limited Liability Company, yet even with such protection its advisable to obtain a suitable commercial general liability (CGL) policy / business insurance.
Under Connecticut law a LLC member is protected from personal liability for the debt, obligation or liability of the limited liability company, whether arising in contract, tort or otherwise or for the acts or omissions of any other member, manager, agent or employee of the limited liability company and a LLC member is not a proper party to such an action. (Conn. Gen. St. Sec. 34-133 and Sec. 34-134).
However, that personal liability protection can be squandered / lost if the member(s) / owner(s) are not careful in how they operate the LLC and/or enter into agreements with others.
Creditors can (and often do) bring claims against a LLC’s individual members by attempting to “Pierce the Corporate Veil”. For example, Limited Liability Company members expose themselves to personal liability for a LLC’s debts when corporate formalities are not followed (i.e. fail to meet, keep corporate records, co-mingle funds / bank accounts), where an individual member so dominates every aspect of the company it becomes his "alter ego" or where the individual has engaged in a tortious act himself or a member entered into agreements before forming the LLC and/or at a time when the company is insolvent.
In addition, even if a member does everything right he/she may oftentimes (especially in the beginning years) voluntarily waive that personal liability protection when they personally guaranty LLC loans / credit applications, etc.
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Disclaimer: The foregoing answer does not constitute legal advice, is provided for informational and educational purposes only for persons interested in the subject matter. Each situation is fact specific and may be subject to state specific laws. Without a comprehensive consultation and review of all the facts and documents at issue it is impossible to evaluate a legal problem fully. This answer does not create an attorney-client relationship.