When broadcasting a tx, a regular node checks for two things: Is the transaction standard, and is the transaction valid.
Standard transactions are, for simplicity's sake, transactions that create p2sh, p2pkh, p2wpkh, p2wsh, and OP_RETURN outputs. A standard transaction must also consume inputs in a few known scripts, namely multisig and regular single key scripts.
The transaction being valid is what prevents your scenario. For a transaction to be valid, a transaction must spend inputs that already exist and are unspent (unspent transaction outputs, or utxos), and the scriptsig for each input must verify. For a standard transaction, this means that the signatures on the tx must validate the script specified at output creation time.
You can try to make a fraudulent tx in two ways:
- You spend coins that exist, but are not your own - In this case, the input validation will succeed, but since you don't own these coins, you cannot sign for them, and the signature validation will fail. The network will refuse to broadcast your transaction
- You spend coins that don't exist - In this case, the network will simply reject your tx with a missing inputs error, since you can't spend coins that don't exist