It's not a relative construction (though some linguists would call it a 'relative clause reduced by Whiz-deletion') but the past participle employed as an adjectival. It is placed after the noun it modifies because it is followed by its complement, and it is bracketed off with commas because it is supplemental and non-restrictive—an additional predication.
It feels odd to you because today we rarely use this construction with intransitive verbs: the participle is ordinarily taken to bear a passive sense, and intransitive verbs of course cannot be passivized. The construction was more common when the perfects of become and verbs of motion were formed with be rather than have; Thoreau 'hears' the full predication as
This outside garment is become indispensable.