What is Surety Company?

Legal Definition
A company, usually incorporated, whose business is to assume the responsibility of a surety on the bands of officers, trustees, executors, guardians, etc., in consideration of a fee proportioned to the amount of the security required.
-- Black's Law Dictionary
Legal Definition
Any corporation organized for the purpose of carrying on the business of becoming a surety on bonds and undertakings. See 162 Cal. 588, Ann. Cas. 1913D, 712, 123 Pac. 808.
-- Ballentine's Law Dictionary