@Hal0persin If you look at the Relay does one of the Wires go to the ECM in the box Blue harness? If it does then I would have to think as it was stated before that it was for an Aftermarket Remote start system.. IF the person left the Relay in the airbox, and didn't give you a Remote start remote I would take a look at the rest of your wiring under the dash. HOWEVER before you do that I would try one thing before thinking you didn't get a remote to start your car... In some cases they could have used a T harness system for your RS, This system would use your Factory Remote.. Press the LOCK button 3 times in a row, Not really fast but not really slow either lol. It should honk the horn and then on the 3 press should turn the parking lights on and then start the car.
If that happens you know the RS kit is still in now just knowing what it is, is the trick. If a good Installer did it, It could be hard to find the Module as it will look like factory wiring.. Even still may be able to look under dash and find the Module. Then you can look it up and see what features it offers. In some cases it is just basic RS and offers nothing special but standard RS. In other cases it could offer the ability to do many different things...
If you find a Box and can't find any info. Post a Pic and I will try and help you with info for the System.. Also in some cases the installer will put a Switch under dash or could be hidden as part of a Valet switch. IF it is off it won't start the car by remote...
IF no switch, and it don't Start with 3 lock presses, I would for sure look under the dash and make sure if they took out the system, that they didn't leave open wires everywhere under the dash... I have seen some pretty bad things in my years of Mobile Electronics. For some it is a blessing because the wiring has been exposed and when making a new install of a RS makes it faster to do the install. However not having one installed and doing something else. Could be a Installers nightmare because lets say you came in to have some Fog Lamps installed and maybe some Neon ground effects. Once a new installer touches the car if they don't repair what was already done before the car came in the new owner may not know it was like that and may think it was left by the person that did the lights...
Look forward to hearing what you find
James