You will likely not be able to use the old cable as a pull. It is probably stapled to the studs.
You could easily remove the existing box, pull a new cable from above and install an old work box. Use a 14/3 cable then you will have separate control for fan and light.
You can tap into the cable coming from the closet to permanently power the receptacle.
You could easily remove the existing box, pull a new cable from above and install an old work box. Use a 14/3 cable then you will have separate control for fan and light.
You can tap into the cable coming from the closet to permanently power the receptacle.