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I just got this car, and the seller had told me about this issue, where the engine turns off if you're slowing down to a stop, mostly if you've been coasting or idling. It has no troubles turning back on again, and although this issue is minor, it's certainly inconvenient. I suspect it may be a dirty IACV or maybe a vacuum leak, but I'm not sure. Does anyone have any ideas? I'm wanting to find out what's causing this problem asap, so I can fix it!

As it's happening at idle, it could be an air leak or idle control valve as you suspect, but it could be numerous other problems too, so needs to be diagnosed by a technician in order not to go firing parts at it in the hope it might be the problem.
In the long run, it's likely to work out cheaper by paying a professional to carry out a proper diagnosis rather than to keep buying parts that are not needed.