That depends on the card and how you acquired it. A corporate Amex is typically backed by the employee, but they are falling out of favor in part because of that.

If you have a corporate card through a bank other than Amex, there’s a very good chance you do not carry the liability for paying it.

Your employer could come after you if they feel it was used improperly, but that’s a very different can of worms than carrying credit liability.