I don't think that Klopp will suffer the same fate as Tuchel, but even if it happens it is of course a loss for Liverpool because it is difficult to find a coach as good as Klopp at the moment, Liverpool deteriorating performance does not seem to be due to Klopp strategy error but none other than because of his performance their players are indeed deteriorating, losing Mane, I think is one of the reasons for Liverpool current bad performance and Nunez has not been able to have an effect on Liverpool game, yesterday defeat against Napoli was quite painful but if we look at Liverpool defenders they performed quite badly in the match.
At the moment even though Liverpool's performance is not very good but I agree with what you say because it seems that the officials still haven't decided to rush to sack Klopp because they are aware that if they sack Klopp they also can't decide who will replace them because in terms of This is actually quite difficult, especially since they also know that this change of coach will not necessarily improve Liverpool's performance.
I see no reason to think that sacking the coach will improve Liverpool's performance. Liverpool has done very well in the last few seasons under Klopp. Liverpool's performances have been poor since the start of this season as they have made several changes to the squad. And the new players haven't adjusted well to the team yet. Klopp needs to be given time, not sacked. Liverpool will be strong again if the new players can fit into the team.