Pulled over right now. Need advice. Bike dies at idle.

TL;DR bike dies without throttle and in neutral or clutch pulled in in gear rarely. Engine hesitates rarely when throttle is turned and a minor loss of acceleration rarely. Only happened once or twice recently since running out of gas 3 times in a week. But now it’s doing it. I suspect fuel system issue.Ok so I’m pulled over on the side of the road right now googling before I damage my engine.Bike is a Kawasaki z125.let my bike warm up for 3 minutes at work and left keeping rpms below 4k for the first few minutes (redline is 10k).No more than 30 seconds later down the street, I hold my clutch and coasting to a stop and the bike just dies at like 20 mph from 40mph. It doesn’t do this every time. And has only done so twice in the past month but it has been happening.After a few minutes I went back and turned the bike on and left it in neutral, let it run for about 30 seconds and the idle was perfect at 1500 and sounded healthy/normal.I gave it some revs to 3k, 4, 5 & 6. Every time it would stutter. This is the first time my RPMs have ever stutteredFor example, I revved to what would be 6k with my throttle turn and it went to 4K, hesitated and then hit 6k and hesitated to come back down.What do you think this is and should I ride it home? The bike will stay on in neutral and it will ride as long as the RPMs are above 2K. And yes there is a loss of acceleration via /r/motorcycles https://www.reddit.com/r/motorcycles/comments/dzw63w/pulled_over_right_now_need_advice_bike_dies_at/?utm_source=ifttt