When a person becomes a lineage student, everybody knows who that individual is and what their relationship with the instructor is.
Should the instructor move away or die, people will look to the lineage student to continue the teaching in the instructor's name.
This is the responsibility of the lineage student.
For example, when Peter Southwood died, several total strangers contacted Sifu Waller to advise that Peter Southwood was dead.
Even though they had never trained with Sifu Waller, they knew that he was Peter's indoor/lineage student.
Peter had made no secret of the fact.