She can be permitted to quit her job subject to the notice conditions laid down in the contract of employment. Of course the employer can decline her buy out option of notice period if any and insist upon her actual service.
If any bond was already executed by her to serve the organization for a particular period after her training abroad or to reimburse the entire cost of training in case of breach and the specified period is not yet over or she is not willing to reimburse, the employer can reject her resignation.
Try to convince her by offering some sops and if not possible, search for suitable replacement. In the realm of employment, no one is indispensable!
Your company could have been a little more thoughtful. Your company should have made legal agreement with the employee before sending her abroad for the training. In this agreement you could have mentioned specific period for which employee must serve.
At this stage, legally your position is not so strong. Beyond compelling her to serve the notice period, you cannot do anything as such.