This is the 8523rd most frequent Japanese word.
抜け出せ
"抜け出せ" means "to get out" or "to escape."
In this sentence, "抜け出せた" is used to convey that he was able to leave or escape from the party.
彼はそのパーティーから抜け出せた。
He managed to escape from the party.
Here, "抜け出せない" expresses the idea of not being able to overcome or escape difficulties caused by mistakes.
その書類の間違いを抜け出せないで困っている。
I am having trouble escaping from the mistakes in the documents.
"抜け出せる" in this context indicates the possibility or effort to escape or overcome fear.