After Solomon had built the temple in Jerusalem (960 B.C.) there was nothing in the Ark except the stone tablets that Moses had put there at Horeb (1 Kings 8:9 and 2 Chronicles 5:10). The NIV Study Bible notes on 2 Chronicles 5:10 say the jar of manna and Aaron’s rod were presumably lost when the Philistines captured the Ark of the Covenant. (See 1 Samuel 4:11 to chap. 6)
Various Bible commentators have pointed out that the tabernacle referred to in Hebrews 9:4 is the one built under Moses. The ESV Study Bible makes this comment:
“By the time of Solomon’s temple, it was noted that there was nothing in the ark except the two tablets of stone (1 Kings 8:9; 2 Chronicles 5:10), but that may suggest that other items had previously been in the ark.”
Some 400 years had elapsed between the time of Moses and Aaron and the Ark of the Covenant being placed in Solomon’s temple. The fact that the Ark had been stolen by the Philistines and it took them some time to return it may mean that the Philistines looted and plundered some of its contents. Perhaps they stole the rod and the jar of manna, though given the plagues that afflicted them wherever the Ark stayed, fear would surely have prompted them to return any pilfered items!
However, Exodus 16:32-34 does not actually say the manna and rod were placed inside the Ark. It says they were ‘placed before the Lord’ in front of the Testimony. This anticipated the later description of the tablets containing the Ten Commandments as “the two tablets of the Testimony” (31:18; 32:15; 34:29) hence “the Ark of the Testimony” for ‘testimony’ is an old-fashioned word for ‘covenant’. Exodus 25:21 simply says that God instructed ‘the Testimony’ to be put inside the Ark – the stone tablets. Now, I may be wrong, but I wonder if it is mistaken to conclude that the manna and the rod were also placed inside the Ark? If I’m wrong, please may someone correct me!
Hebrews chapter 9 states that the Holiest of all in the tabernacle contained the golden censer and the Ark of the Covenant. In the Holiest part of the tabernacle was also placed the golden pot of manna, Aaron’s rod that budded, and the tables of the covenant. This was with regard to the tabernacle and not the temple in Jerusalem. And it does not need to imply that the manna and the rod were inside the Ark; all those items were in the Holiest part, but not necessarily all inside the Ark. The censer was not inside it. The other items (apart from the stone tablets) need not have been inside it either.
My answer, therefore, covers both contingencies – that the manna and rod were inside the Ark, then stolen by the Philistines, but my own view is that they were never inside the Ark and that Exodus 16 and Hebrews 9 do not necessarily imply that they were.