You should know that Erik ten Hag was successful in his first season at Manchester United, because Erik ten Hag managed to make Manchester United finish in third place in his first season. Therefore, even if, for example, Erik ten Hag was at Chelsea and was successful like that in his first season, then of course Chelsea would not sack him either.
Chelsea is not like Manchester United, the owners don't give second chance and they're not relenting when the appointed coach in charge looks incompetent. Todd Boehly sack Mauricio Pochettino and was bad news for the Blues because Mauricio Pochettino have sealed the europa spot but couldn't convert his chances. Manchester United hooked up with Erik Ten Hag because he was the man for the job. He deliver quite exceptional tasks for the growth of the Red Devils. Erik Ten Hag would have been successful in Chelsea.
But they will most likely keep Erik Ten Hag despite his poor performance this season. For the first season, it was a good thing that he could show because he was able to bring Manchester United to a top-flight finish, but this season he is in the middle of the table, and actually compared to Chelsea, both of them should have fired their coaches, even Erik Ten. Hag led Manchester United to win the FA Cup.
However, each team's management decisions are different, some make the decision to fire and some don't. This is completely their decision, because maybe on the other hand Manchester United wants to give Erik Ten Hag more opportunities. It's just whether Erik Ten Hag will answer with a good performance or not.