If I lose control of a location, what happens with my hidden cards?

When you lose control of a battlefield, any hidden card you had there is sent to the trash (Rule 107.3.d, Rule 811).

There's one important timing exception: during a Combat Showdown, you maintain control of the battlefield until the showdown fully resolves, even if all your units are removed. This means you can still flip and use your hidden card as a Reaction during that window. Outside of combat, losing your last unit causes immediate loss of control and the hidden card is trashed with no opportunity to react.