My cousin opened up a part of the wall at his house, only to find open splices. Every electrical splice must be enclosed in a junction box. It can be metal or plastic, but it must be accessible (in case the splices need to be checked or reinforced later on). My recommendation for this situation is to re-run sheathed romex to the last receptacle on the circuit. This solves two problems. It brings the splices into the box shown here, and it protects the wiring all the way to the next receptacle. I'm guessing that the last outlet was an afterthought because the rest of the circuit is enclosed in conduit.
