We analyze Hubble Space Telescope observations of nine Large Magellanic Cloud star clusters with ages of 1-2 Gyr to search for evolved counterparts of blue straggler stars. Near the red clump regions in the clusters' color-magnitude diagrams, we find branches of evolved stars that are much brighter than normal evolved stars. We examine the effects of photometric artifacts, differential reddening, and field contamination. We conclude that these bright evolved stars cannot be explained by any of these effects. Our statistical tests show that the contributions of photometric uncertainties, crowding effects, and differential reddening to these bright evolved stars are insufficient to fully explain their presence. Based on isochrone fitting, we have also ruled out the possibility that these bright evolved stars could be reproduced by an internal chemical abundance spread. The spatial distributions of the bright evolved stars exhibit clear concentrations that cannot be explained by homogeneously distributed field stars. This is further confirmed based on Monte Carlo-based tests. By comparing our observations with stellar evolution models, we find that the masses of most of the bright evolved stars do not exceed twice the average mass of normal evolved stars. We suggest that these bright evolved stars are, in fact, evolved blue straggler stars.