You global investing accounts are held by brokerage and clearing services providers. The custody of your account is managed by some of the largest banks and clearing firms in the world. If WealthBullet or Stockal goes down, your account will still be safe and secure with them and you will be able to access it and/or move it to another brokerage firm as you please.
Additionally, you also have automatic insurance on your US investing account. Read more about this here.