They will probably use secure elements (a small, tamper-resistant chip in your phone) and limit transaction amounts when you’re offline. As long as the other party has an internet connection, it will be impossible to double spend. There may also be a warning about an increased risk if you attempt an offline transaction. However, if there is no internet access and the fraudster is able to inevitably spoof/emulate/attack a secure element, the security mechanisms would fail and a double spend would be possible. This will be detected as soon as internet access is available again. As it requires a personal presence, the police should be reasonably capable of fighting such crime.