It is yours. Again, you can't back with "deposits". If you have deposits, the depositors have a claim that encumbers the assets; you can't then "back" something with encumbered assets. You can only back a currency with unencumbered assets. And if you have unencumbered assets, why would you use them to back a currency?
And if people redeem from you, just add a clause where if the liquidity pool is gone you have to wait X days before getting it redeemed.