The signature signs the spending transaction(*). Modifying it in any way will invalidate the signatures in it.
(*) Not actually, as it's obviously impossible for the signature to sign itself. There are also means for a signature to indicate it explicitly does not sign certain parts of the transaction, permitting those to be modified after the fact.
When you spend Bitcoin in a transaction, the transaction must reference at least one existing unspent transaction output (UTXO) and provide a valid signature proving that you are authorized to spend it. The transaction then consumes the UTXO in the inputs, and assigns value to newly created UTXO in the outputs.
Other network participants running a type of ...