The only conceivable scenario where a major Canadian bank fails and any depositors are not made whole is one where the government has lost the ability to maintain the currency and the Canadian dollar is worthless anyway.
[0] https://en.wikipedia.org/wiki/List_of_largest_banks_in_North...
The mutual fund would use the cash to buy stocks or loans and you would be entitled to a share of that profit or loss (both upside and downside), but the mutual fund manager would typically only be paid an annual fee (1).
Money deposited in a bank gives you no upside, and, as you say, a tiny downside risk. (even before deposit insurance) Those taking the downside risk (as well as the upside) is mainly bank equity investors.
(1) As another commenter correctly pointed out there are also other sort of funds that look a bit more like banks for various reasons, but that also doesn't necessarily mean the fund manager is the one taking the upside/downside risk.