I my car "exhales" when I turn it off?

I have a 2002 Ford Explorer, 6 cyl with approx 120K miles on it. It has begun to idle a little rough despite a tune up 20k miles ago. Now it has begun to “exhale” when I turn it off. The engine dies and then appears tp “exhale”.

Nobody knows what you mean by “it exhales.” Got anything else for us?

This may be a vacuum canister releasing. There is a vacuum chamber in the power brake booster, also.
Open the hood, with the engine running, turn the engine off and listen. After turning the engine off, press the brake pedal. If the car is on a slight incline, hand brake off, transmission in neutral, the foot brake, when lightly pressed, should hold the car. If not, it has lost it’s stored vacuum. The repair would be to replace the brake power booster.
Loss of vacuum, through the power brake booster, can cause the engine to idle rough. For the engine, it’s a vacuum leak.

Thank you! I appreciate your expertise and quick response!