Fetching details from the dictionary...
to exist; to remain; to live
to consist (in); to lie (in); to reside (in); to rest (with); to depend (on)
to retain; to preserve; to keep
責任は当事者に存した。
The responsibility rested with the parties concerned.
問題は別の次元に存している。
The problem exists in a different dimension.
この地には数百年にわたり守られた伝統が存する。
In this place there exists a tradition that has been preserved for several hundred years.