a single thread that exists only to ditch the rest of the rope.
means A single thin filament — of hair, thread, rope, or wire — or, as a verb, to leave someone abandoned with no way to get back.
from Two strands of meaning twist together here. The 'filament' sense is old and murky — likely Old French 'estran' for a rope-cord — and English seized on it for any single thread teased out from a twist. The 'abandoned' sense comes from a different root entirely: Old English 'strand,' the shore or beach, related to the same word across the Germanic seas. To be 'stranded' was literally to be a ship run aground on the sand — left high and dry by the tide. The two words, unrelated, eventually shared a spelling, so now a lonely thread and a marooned sailor wear the same name.