LAX-IAH-EZE - bags properly tagged at LAX for EZE via IAH

I usually will check/track the bags once boarding in Houston just as something on my checklist

i noticed that one of the 4 bags (2 people on itinerary) was not put on the plane with the other 3. Kept checking and eventually saw the 4th bag

However, when we arrived EZE, there was no UNITED bag tag on that luggage - just wondering what may have happened to it - and how did they know that bag was supposed to go to EZE?

I doubt it fell off , but I guess its possible. Also maybe possible it came off when it was placed (late) on the EZE flight

If a tag falls off in Houston, how the heck would they know where to put it?