Before magnetic tape became the standard recording medium for flight data recorders, most FDRs used a long strip of metal foil that had altitude, airspeed, etc. traces scratched into it by a set of styli inside the FDR (although a few very early FDRs used wire recording instead). Judging from a number of NTSB accident reports that mention FDRs where the foil had run out and been taped down at the end for maintenance, this presumably wasn’t a continuous loop of foil (although I can’t imagine it would have been hard to implement a continuous-loop system; it seems to me that, to make such a system workable, all you would have had to do would have been to squeeze the foil through a set of metal lips to flatten out the old traces just prior to passing under the sticks), but, instead, one that had to be removed and dealt with by maintenance when it ran out. When a foil FDR became full and was removed for maintenance, were the traces flattened out of the foil and the foil reused, or was the strip of foil replaced with a new, empty strip (with the full strip presumably being either discarded or possibly stored in an archive somewhere)?
Those older FDR's are known as "foil oscillographic recorders." This technology is similar to the old recording barometers, which were used for, among other things, providing evidence of altitude in glider record-attempt flights. Just as in these barometers, the recording surface was not reusable in those FDR's. When it would run out, it needed to be changed. The FDR's had an indicator which showed how much usable foil was left in terms of hours. The rolls of foil were 200 ft long and ran at 6 inches per hour when the aircraft was operating, about 400 hours' worth. This was an inspection item on the aircraft.
In addition, the foil was made of Inconel, which is known as a "superalloy" that is resistant to very high temperatures. It would be very difficult to remove the tracings of data without specialised equipment, and in reality the tracings removed material from the protective surface coating on the foil. If you recycled it the quality of the data could be impacted by corrosion.
This very cool video illustrates how these FDRs worked.