He wasn't sacked at Dortmund and he wasn't forced out. He made his resignation public after they had already steadied the ship and he finished the season inside the EL ranks (not a bad finish, considering the team hit rock bottom halfway through the season) and reaching the cup final. After so many years with largely the same squad things had gotten stale and it was either him leaving or the club breaking up an otherwise pretty good squad for the sake of changing things up and giving new impulses. At the time him resigning was the logical option, because the alternative wasn't feasible for Dortmund economically.
It's pretty much the same situation at Liverpool, isn't it? They added players here and there, but the core of the team has played under him for many years, they had their success together and maybe it got a bit harder to motivate themselves for the daily grind - playing the same football, for the same club, under the same coach with the same team mates and they don't have the money to just make big transfers for the sake of creating a new itch.
Unlike at Dortmund most of their (former) top performers are around 30 now, so if Klopp himself is still motivated I could see them stay with him and try to start another cycle, but getting rid of the old guard.