Yes, a divorce case in Chennai can absolutely continue even if one party moves abroad during the proceedings, since Indian family courts retain jurisdiction over matters properly filed before them, and a party's subsequent relocation, while creating certain practical challenges around service and participation, does not divest the court of its authority to continue hearing and ultimately deciding the case.

If the party who has moved abroad is the respondent, service of court notices and summons must be properly effected through appropriate channels for international service, such as through the Ministry of External Affairs, registered post to the overseas address, or increasingly, through court-approved electronic means including email, ensuring the relocated party receives proper notice.

The party residing abroad can continue to actively participate through several mechanisms, including engaging local counsel, appearing via video conferencing where the Chennai court permits this arrangement, or appointing a power of attorney holder to manage certain aspects of the litigation on their behalf.

If the relocated party fails to respond despite proper service, the court can proceed ex-parte, deciding the matter based on available evidence, though this outcome is generally avoidable through proper engagement of counsel. Consulting the team at Aapka Legal Advice can help you navigate the practical and procedural aspects of continuing your Chennai divorce case when one party has relocated abroad.

Given the additional complexity that international relocation introduces to service and participation, obtaining a second opinion from a retired judge on how best to manage your specific cross-border situation can provide valuable strategic guidance. Chennai's experienced family law advocates and retired judges, available through Aapka Legal Advice's Chennai divorce lawyer directory, regularly assist clients with these cross-border matrimonial matters.

In conclusion, a divorce case in Chennai can indeed continue to completion even after one party moves abroad, provided the procedural requirements for international service and remote participation are properly navigated.