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.
In Chelsea i don’t think its about where they finish rather about winning trophies and instilling a good play in the team. If the overall performance is good then the owners will believe the project is promising and can deliver in a few years. With Pochettino performance this season i don’t think the team looks ready to challenge for the title that why they replaced him.
In Ten Hav situation, if he were to be Chelsea’s coach he will definitely be sacked despite winning the FA cup because the team doesn’t look ready at all and it’s almost as if he is not teaching the players anything or has a specific style of play at all. Pochettino was even better and he got sacked so if Ten Hag was to be a Chelsea coach he would have been sacked mid season.