Bring figs, vinegar, and sugar to a simmer in a large saucepan. Cook, stirring occasionally over low heat, for 10 minutes. Cover, and let cool completely.
Working in batches, puree mixture in a food processor until smooth.
Strain through a fine sieve into a large nonreactive bowl.
Line sieve with cheesecloth or coffee filter, and place over another large nonreactive bowl. Pour strained mixture into sieve. (Do not press solids in sieve.) Cover with plastic wrap, and let mixture strain in refrigerator overnight (or up to 2 days).
Uncover, and remove sieve from bowl. Discard solids. Pour vinegar into a resealable nonreactive bottle or jar.