Omega cause idle problem? (empty controller is not)

Hello, my friend bought Omega 2.0 16 v, automatic, 110tkm, year 11/1997, model 1998. There is the following problem: if you slow down strongly and go down the speed, the engine goes off, which you can start directly again. If you give a short gas just after more braking, the engine does not run out. Otherwise everything is ok. Idle control is not, normal hoses also not. The previous owner of the car says that at Opel Werkstatt you have said that the sensor or idle control My question to you, please: Does anyone know what part can really be meant, what exactly does that mean? If it wasn’t the mentioned part, what else would be the cause? Thank you, and a pleasant weekend for everyone. Greetings: If you were not able to find the right place, please do not hesitate to contact us.