If you commit an act or accrue a debt that normally your individual assets would be shielded from having to pay as a member of an LLC, each of the individual members of the LLC are then on the hook for such debt until the debt is paid plus any accrued incidental costs of collection. The LLC is no longer there to shield your personal assets and someone could take your house, your business assets, and private property or individual assets to satisfy the debt.
Like all matters governed by state law in the United States, the consequences of not registering as a foreign company in a state where an LLC does business varies from state to state.
In most states, the primary consequences of failing to file are that you are not allowed to file lawsuits or counterclaims in court until you bring your LLC current, and that you are not eligible to licenses in the state. An inability to get a license can be particularly a problem in a licensed industry or occupation, and in situations where there are state withholding taxes that usually require a license to be in full compliance with.
Generally speaking, failure to file a foreign company registration will not cause your company to lose limited liability protection or the right to defend the company against someone else's lawsuit.