My idea for a solution?
Have an option within the app for each person to set an identity password, this is auto used on joining of a game session. If no password is set, user is prompted to create a password or set a temporary password.
If the identity then falls during the game, players are given the option to enter the password to take control of the identity.
Failing this, it could be either put to a vote to all players or up to the game creator to assign the fallen identity to another player. If its the game creator.. the second person to join the game and so on or again, down to a vote.
For further security it could require the password for all transactions, making the password simple like a pin code would keep things quick.
I only suggest this as there are loads of reasons for batteries dying even if you know its low, if you get an important phone call, you go out for a smoke break (I dont smoke, thus people go out of my house to smoke) or if people are drunk and just dont notice. Additionally.. if you're like my fianceé you have a tendency to drop your phone into cereal and brick it.
Could also add an option for any player to alert the game session that another player is no longer there or has been disconnected due to fault and requires a takeover, therefore avoiding the need to keep the app open at all times and allow for identities to save battery by being disconnected but remaining idle.
Another game function that allows an identity to be re-taken over to another device using the same pin.