to pull through
Webster's Dictionary (GCIDE)
Pull \Pull\, v. i. To exert one's self in an act or motion of drawing or hauling; to tug; as, to pull at a rope. [1913 Webster]
To pull apart, to become separated by pulling; as, a rope will pull apart.
To pull up, to draw the reins; to stop; to halt.
To pull through, to come successfully to the end of a difficult undertaking, a dangerous sickness, or the like. [1913 Webster]