Final answer:
No, the check hasn't been negotiated to Greg. Signing the back of the check without a valid endorsement does not constitute negotiation. Eve could have avoided this loss by taking additional precautions.
Step-by-step explanation:
No, the check hasn't been negotiated to Greg. In order for a check to be negotiated, it needs to be transferred to another party with an endorsement. In this case, Greg signing the back of the check beneath Eve's signature and cashing it does not constitute a valid endorsement. Eve could have avoided this loss by taking additional precautions, such as keeping her paycheck in a secure location or depositing it directly into her bank account instead of cashing it.