What happens to my money invested in mutual funds through coin if coin goes down one day?
Coin is only a platform from Zerodha from where you can invest in mutual funds. The mutual funds that you invest in through Coin is essentially kept in demat account with CDSL. So your revised question should be what happens if Zerodha goes down.
In that case, Zerodha Securities Pvt Ltd is a Depository participant with CDSL being the depository. In the most unlikely event of Zerodha going down, the holdings, be it stocks, mutual funds or other securities are still with CDSL.