The word sprung in the OP's context implies 'fitted with a wound spring'.
The trap operates by unwinding the spring on a trigger.
It is common to refer to the device itself (in any state) as a 'sprung trap' -- Buy a sprung trap. ; Use a sprung trap to catch a mouse.
Nice idea indeed (but sprung means 'not sprung'):
I've seen in the past it might take several try's (tries) to get a set trap
'operational'. 'Course a sprung trap, allowing the mice to clean it
out will give them a false sense of security. Let 'em eat for a day or
so and then set the trap.
This one gone a waste (smart rats or lucky ones):
I have also come back to find a sprung trap, nothing in it, and a large dead pack rat close by. Guess it hit them on the head, and they didn't stay in the trap.
Sprung means 'unsprung':
Overnight, rodents are lured into the traps by tantalizing peanut butter/oat scents and step on a trigger that sets off the trap. Early the next morning , we check each trap. When we discover a sprung trap, we carefully empty it into a heavy plastic bag