They were born in Saudi Arabia but for some reasons their passports were never made. They were on their mother's passport earlier as kids who was a Pakistani (she has passed away) . Now they are 18+ of age and have applied for an Indian nationality as father is an Indian. Waiting for 5 years now. Can they travel anywhere?
They might manage to get to neighbouring countries by road but have little chance of getting on a commercial flight without a passport. I don't recommend doing this because it is likely breaking the law.
Given they were previously named on their mother's Pakistani passport this might mean they have a better chance of getting a Pakistan passport of their own more easily than getting an Indian one.