Virginia employer terminated employee and wants signing bonus returned
Can the employer legally keep his last check and send the employee a bill for the remainder ?
No, unless (1) the employee resigned and (2) his resignation does not amount to constructive termination. The employer may withhold the remaining $7,000 only if the employee did not meet the condition of "30 days of employment with xxxxx".
Absent any language to the contrary, the requirement of "1-year commitment" is to be construed as the consideration expected from the employee (namely, "not to quit") in exchange for the bonus. Termination by the employer is self-defeating in the sense the employer himself made it impossible for the employee to fulfill the consideration that was expected from the employee. Therefore, the employer forfeits his entitlement to reimbursement.
In the event that the employee met the condition of "30 days of employment with xxxxx", he would be entitled to the remaining $7,000 as well.
Virginia labor law has no provision for treble damages (this is in response to one of the comments, per the OP's suggestion). The statutory provisions are only a civil penalty no greater than $1,000 for each violation, a portion of attorney's fees, and "all wages due, plus interest at an annual rate of eight percent". See Code of Virginia at § 40.1-29 A.2, F, and G. Item E of that statute determines which violations are misdemeanors and which are felonies. This statute would be applicable only if (1) the employer disavows the employee's entitlement to the remaining $7,000, and/or (2) the employer withholds a portion of the employee's earned compensation in an attempt to recover the initial payment of $3,000.