How does the Home Office deal with a mixed Indian-Pakistani couple where neither can get a visa for the other’s country? Should they be allowed remain in the UK together?

How does the Home Office deal with a mixed Indian-Pakistani couple where neither can get a visa for the other’s country? Should they be allowed remain in the UK together?
UPDATE: The Indian High Commission is no longer issuing applicants with Non-Acquisition of Indian Nationality Certificates (NACs). It is now necessary to apply to VFS