In a few words: carry two wallets, an empty one with a driver's license, an old bank card and let's say $12 and your real one somewhere else, in your backpack perhaps.
You want to have in that fake wallet enough for the police to accept it and not too much to avoid feeling bad about it. This should be a sum you're happy to give away in order to avoid a bigger one. This trick also works for a robbery but I hope I nor you will make it there.
I learned this the hard way.
We buzzed out of our home stay in Ubud, Bali at around 10 am, headed for a visit of Mount Agung. Ubud has many one way streets and with the small scooters we were riding it was an easy thing to go against the traffic. Many other people were doing it too. At the end of the street, the police was waiting and fetched us.
They called me to the bureau first and the officer said:
"No international drivers license, take one way street. You make two mistake, you pay 250000 + 500000."
My jaw nearly hit the desk.
I had just withdrawn 1.5 million Indonesian Rupiahs, around a $110 as of today. I had the money there, in my pocket. I could pay and was free to go.
"Give me a sec I'll speak with my friends."
He said "Okay" so I supposed it was open to offers. In poor countries everything is negotiable, even the police.
I walked out, had my friends group in front of me to block sight and stashed most of what I had withdrawn in my back pocket. I went back and we settled for 250000, around $18. A bit steep but it's the third of what was intended. I messed up not having less as he would have gone for it but I also didn't want him to escort me to the nearest ATM. I would have had to pay the full price. The money obviously went straight to his pocket and we received no receipt.
For next time I know, I have a secondary wallet with me containing only a couple dollars.
In poor countries everything is negotiable, especially the police.