How to protect exposed bathroom fan wiring
If you cant find a replacement cover, you will have to make one. Easiest way is to get a 2x4 or a 4x4 metal cover (preferably with a 1/2" knockout in the middle). Bend it into an "L" shape, and then attach it with short self tapping sheet metal screws. 

To attach power, you will need a couple of pieces (links below, you can probably find these at your favorite hardware store): 
EMT (existing conduit) to FMC (flexible metal conduit).
A short piece of FMC (hopefully your wire is long enough)
FMC to 1/2" knockout (this will connect to your cover if it has a knockout otherwise you will have to drill a 1/2" hole

Please note that these links may not be the correct size of connector, but represent the type of connector. Please also read  ThreePhaseEel's note below about grounding

https://www.amazon.com/gp/product/B000KKVUUE/ref=crt_ewc_img_dp_1?ie=UTF8&amp;psc=1&amp;smid=ATVPDKIKX0DER

https://www.amazon.com/Southwire-55082121-Aluminum-Flexible-Conduit/dp/B002LT0M4W/ref=pd_bxgy_img_2/143-0060259-1607946?_encoding=UTF8&amp;pd_rd_i=B002LT0M4W&amp;pd_rd_r=8913bc2a-d3d9-4207-bd70-24f159c7959c&amp;pd_rd_w=3Sk1R&amp;pd_rd_wg=lkVjo&amp;pf_rd_p=4e3f7fc3-00c8-46a6-a4db-8457e6319578&amp;pf_rd_r=VNNJ09YK37FJZQ9VQCFV&amp;psc=1&amp;refRID=VNNJ09YK37FJZQ9VQCFV

https://www.amazon.com/Halex-20421-2-Inch-Squeeze-Connector/dp/B006X15ZWS/ref=pd_lpo_60_t_0/143-0060259-1607946?_encoding=UTF8&amp;pd_rd_i=B006X15ZWS&amp;pd_rd_r=51ae619f-ed25-4856-a7c9-c5cdaee4fd3e&amp;pd_rd_w=qsDiY&amp;pd_rd_wg=Z6IJb&amp;pf_rd_p=7b36d496-f366-4631-94d3-61b87b52511b&amp;pf_rd_r=DTK6KWNNB17N7TBWBJ4D&amp;psc=1&amp;refRID=DTK6KWNNB17N7TBWBJ4D