My question is: What happened to the cross that Jesus died on?
No one knows for sure. Chances are it was used again for other executions, since wood was very scarce in Jerusalem. It’s likely that Jesus carried only the cross beam to the site of His execution. Then, after His wrists were nailed to it, the beam would have been hoisted up and fastened to a vertical pole already fixed into the ground. Then His feet were nailed to it. This would have permitted multiple uses. From time to time various groups have claimed that they have part of the Lord’s cross, but no one can prove them right or wrong.