In your sentence, “that” is actually used to give more information about the adjective “closest”. It isn’t really used as a relative pronoun; it is used to introduce a noun clause acting as an adjective complement.
“that anyone will come to understanding” is a “noun clause” giving more information about the adjective “closest”.
It is the same structure if I say:
I am afraid that anyone will come to understanding my answer.
“Afraid” is an adjective, and the “that” clause gives more information about the adjective “afraid.”
“That” is optional in this case.
I’m afraid anyone will come to understanding my answer.” is correct, as well.
If you write the sentence until “closest” and put a full stop after it, the sentence still makes sense. It has less details, but it is still a complete and correct sentence.
“Understanding” here, is used as a gerund because “come to” is a phrasal verb which has many meanings, but in this case, it can be understood as “to get” the understanding.
This is similar to “look forward to” + gerund.
Hope that makes sense.