A player never getting run out in his career is one of the biggest achievements for him. Even if the player is fit or young, there can be changes in the field where because of miscommunication with the batting partner, he can be dismissed because of run-out.
Well, you would be thinking there can not be such players, but here, we have named five players in cricket history who have not lost their wickets while running between the wickets.
Five Cricketers Who Were Never Run Out
Peter May:

Former England great cricketer and captain Peter May was the cricketing Prodigy during his school days. He is considered as one of the finest batsmen of England in the 50s. May was a classic batsman and a strict leader.
Having made the debut for England in 1951, the defensive batsman went on to represent his side in 66 matches (106 innings). He amassed 4537 Test runs, including 13 centuries and 22 half-centuries. May holds a unique record of never getting run out during his illustrious career, which spanned for over a decade.
After retiring from the game, May also umpired in a couple of matches for ICC.