The May rules (available on the GMT website) indicate that a force that has a source of provisions need not roll for surrender (but still gets a foraging marker).
DEFINITION OF SOURCE OF PROVISIONS: Any space (other than an Island or Coastal Fort) that is neither enemy-controlled or adjacent to an enemy SP is a Source of Provisions. Any Isolated unit or group of Isolated units that is either located within, or can trace a LOC of any length (between friendly Depots) to, such a hex does not have to roll for Surrender. Except Fort Morgan and Fort St. Philip/Jackson, Isolated Confederate Coastal Forts (and the units within them) may not use a Source of Provisions unless their associated Ocean Port is Confederate-controlled. Isolated Naval Units need to be located at, or able to trace a Supply Path to, a friendly-controlled port that qualifies as a Source of Provisions.
In effect, the Cav must be tightly surrounded before needing to roll for surrender. Note that even 1sp ZOIs can prevent Cav from avoiding battle or retreating. Check also the union militia rules, they also help against cav raids.