Is is permitted to fish nonmetallic cable through walls?

I have flexible metal conduit that appears original to the (1948) house, containing fabric type conductors. the circuit to the outlet in question drops from the attic and doesn't appear to be stapled, just secured inside the box. I have tried pulling the wire out so I can replace it with THHN, but it won't come out. As I pull out the FMC, can I just pull in the Romex? I know NM cable is usually requires to be stapled within 6 inches of a box, but wouldn't the securing mechanism in those old boxes be acceptable? I have been looking through the NEC but haven't found this answer yet.

◄WhoMe►2019-09-27T12:33:10Z

In some areas it is. Check your local code to be sure. Here in Dupage Illinois, yes. I ran into that same stuff. You'll never pull those conducters out of that old BX, stapled or not.
The rule here is Romex has to be covered by the finished wall, none can be exposed in living areas. Only in the attic and at the load center.