When you are "cleared for an approach", you are authorized by the FAA rules to make any headng or altitude changes nessary to accomplish the approach so as long as you conform to the minimun restrictions of the published approach (jeppesen for example).
NO NO NO!!!
When cleared for an approach, you are NOT cleared to descend below previously cleared altitude UNTIL you are ESTABLISHED on a published section of the approach! See FAR 91.175(i):
"When operating on an unpublished route or while being radar vectored, the pilot, when an approach clearance is received, shall, in addition to complying with Sec. 91.177, maintain the last altitude assigned to that pilot until the aircraft is established on a segment of a published route or instrument approach procedure unless a different altitude is assigned by ATC."
In the OP's example, flight A may NOT, without EXPLICIT further clearance, descend below 6000' until passing FIX and established on the approach!