Battery hull/foil damaged while changing display of a smartphone
The metallised foil forms part of the gas and vapour barrier of the cell and is there partly to keep moisture and excess oxygen out.

If you reseal the breaks perfectly the battery may still last a while but no way to know how long as the amount of atmospheric moisture that has entered is impossible to determine.

If you leave the breaks open and there is no other barrier inside the battery will surely fail.

I would not place that cell into a phone of mine that is ever left unattended. 

I might solder a resistor and an LED onto it and use it as a torch while it has charge but keep it stored outside in a clay pot or metal tin until eventual disposal. 

There are many descriptions of damaged Li-Po cells overheating and sometimes catching fire but there are also those tortured cells where only some heat was generated.  The amount of remaining charge also affects the amount of energy inside that can be released from a short circuit.  The amount of lithium is generally small so the danger from a discharged battery is less.