Researchers from two universities in Switzerland gathered two groups of participants (Germans), and gave them to learn at 10 pm a Dutch-German word series. Some of them were told to sleep, while others were told to stay awake. Both groups were exposed to an audio sequence in which the words to which they had already been exposed were repeated. At 2 o’clock in the AM they were given a test. The group that “learned” during sleep performed better than the one that was depressed by sleep. (via Forbes)
A small mention that I would like to add to this study is that the participants were given to learn new words in Dutch, themselves being native speakers of German. Dutch and German are very similar, as are Portuguese and Spanish or Danish and Norwegian. A study has not yet been conducted in which participants were given to learn a language very different from their native language, for example Arabic for English speakers.
So yes, you can repeat the words you learned earlier in your sleep. But can you learn new words? Definitely not. Although it is almost certain that you can learn during sleep (whether it is about REM, light sleep or deep sleep), it is very unlikely that you will learn new things, whether it is about new words in a foreign language or anything else.
Sleep is important for memory consolidation. Especially REM sleep, a part of sleep that usually takes place in the first 90 minutes of sleep, and accounts for 25% of total sleep. During REM, brain functions are almost the same as when you are awake, whereas physical functions are almost nil. REM is also believed to be beneficial for learning and memory. It is also thought to contribute to brain development in children. A lack of REM sleep may have adverse implications for emotional and physical health.
However, it is not certain whether you can reinforce the words learned during the day. Although it is clear that while you sleep, your brain reviews the information accumulated during the day, it is still unclear whether sleeping while listening to an 8-9 hour tape in which words are repeated helps you. Remember, the subject of “learning” a foreign language during sleep has only been addressed by a few scientists in recent decades. None of them can say with certainty that revising words during sleep through an audio lesson helps the learning process, let alone how much it helps you.
Audio lessons made especially for language learning while sleeping? Fortunately, I do not know of a company that SELLS such courses, probably because this method is not scientifically proven. There are, however, many Youtube channels that offer such lessons in different foreign languages. I think that, since they are completely free, you should try this method at least for a short period, to see if it is successful.