Anything is possible with bitcoin.One day the price is very high and the very next day the price will fall.As we can see the graph of previous months ,this situation can be possible.Falling down to 4000 dollar is very common.But their is nothing to panic.Bitcoin will recover and soon it will reach a great height in coming years.
Yes, bitcoin is unpredictable, it can rise and fall in so far as no one thought, Therefore, I agree that he may theoretically fall to such a limit , I do not even think personally that this will happen