What is being unmatchable?[]
Unmatchable elves do not have the information needed for the matchmakers to create matches for them. Because of this, the unmatchable elf does not receive a match list, nor are their names on another elf's match list.
Why are some elves unmatchable?[]
Presumably, all elves who do not know who their both of their genetic parents will have the Unmatchable status. This is in part due to the Matchmakers striving for genetic diversity; if they do not know who your parents are, you may end up matched to a distant relative or with someone that is not compatible. Sophie is the only elf with this status, because she doesn't know the identities of both her biological parents.
How to get rid of the unmatchable status:[]
In order to become matchable, all of an elf's genetic information must be known and in the matchmaker's system.
Known Unmatchable Elves[]
Sophie: Because Sophie did not know who her biological parents are, she was unmatchable.
So far, Sophie is the only known unmatchable elf, as she is presumably the only elf who does not know who her genetic parents are.