In term of extend and relocate your light fixture. There is no problem if you do that. However, it will not pass the safety inspection. (If you called for one and they see it). And/or it may affecting the house insurance coverage if some bad thing happen that cause by the wiring connection.
And for safety reason, if using type and hide it in the wood is not safe, electrical type is only a thin layer of plastic or rubber, after long period of time it will peel away from the copper wire and contacting the 2x4 wood which have certain amount of moisture. It may cause a “electrical current leakage” which become a short curcuit, the wire will be over heated, it is a fire hazard. My word to you, finish it as professionals will do., the box is $2 or less
And for safety reason, if using type and hide it in the wood is not safe, electrical type is only a thin layer of plastic or rubber, after long period of time it will peel away from the copper wire and contacting the 2x4 wood which have certain amount of moisture. It may cause a “electrical current leakage” which become a short curcuit, the wire will be over heated, it is a fire hazard. My word to you, finish it as professionals will do., the box is $2 or less