If a showdown results in both players having a unit still alive, what happens?

According to the Riftbound rules and the provided FAQ, if both players have units remaining at a battlefield at the end of combat, the attacking units are recalled to their base.

According to FAQ 3022 and Rule 444.1.a.2:

• Ruling: If both players have units remaining at a battlefield at the end of combat, the attacker's units are recalled to base.
• Sequence:
  1. Combat resolves with stunned unit(s) not dealing damage.
  2. If units from both players remain alive at the battlefield after the damage step, the attacker's units are recalled to base.
  3. The defender retains the battlefield.

Important Nuances:

• Recall: Per FAQ 3001, recall does not exhaust a unit by default unless the effect specifically states "recall exhausted."
• Control: As noted in Rule 444.2, if no showdown or combat is staged at the location after the cleanup, the player with units remaining there establishes control. In this specific scenario, because the attacker's units are recalled, the defender remains the only player with units at the battlefield and thus retains control.