When you invest with Wealthsimple, your assets are actually held by SEI Investments (Europe) Ltd., Wealthsimple's UK custodial broker. In other words, SEI executes trades and is where your assets are held. SEI is a leading global custodian of assets, listed on the US NASDAQ exchange since March 25, 1981, under the symbol SEIC. They look after $468 billion of client assets (as at end 2016) and are regulated by the FCA in the UK.
In the extremely unlikely event that Wealthsimple were to go out of business, your account would remain safe and be largely unaffected. All securities are registered in your name, and if we were to close, you could choose to transfer it to a new advisor or redeem for cash to your bank account.