A Notice to Stakeholders was recently published on the website of the European Commission, DG Justice and Consumers, regarding legal repercussions which need to considered (if and) when the United Kingdom becomes a third country.
As of the withdrawal date, UK incorporated companies will be(come) third country companies and therefore not automatically be recognised under Article 54 TFEU by the Member States. They may, however, be recognised in accordance with each Member State’s national law (private international law rules concerning companies and the subsequently applicable substantive company law), or international law treaties.
As a consequence, depending on the applicable national or international law rules, such companies might not have a legal standing in the EU and shareholders might be personally liable for the debts of the company. The full notice, which deals with other important aspects of EU company law, can be read here.