What exactly do you mean by fake Bitcoin? Actually, there are some fake Bitcoin it was in the ETH network which is wrapped BTC.

If you were talking about zero fees then no pool will include your transaction to confirm it will be stuck on the mempool unless if you own a miner and are mining on f2pool you can request to them to include your transaction to mine.

And I think doublespend is what exactly you talking about you receive a zero fee transaction and then it stuck unconfirmed and the sender made another transaction with a fee to a different address that you didn't own and the BTC you received never confirmed.