Questions & Answers about Den overlevende er trygg.
Here, den works a bit like the.
In Norwegian, when an adjective or adjective-like form stands by itself and refers to a person or thing, you often use den, det, or de in front of it. So:
den overlevende = the survivor / the surviving one
This is very common with words that describe a person by a quality or condition, such as:
den skadde = the injured person
de rike = the rich
So den is not random here; it helps turn overlevende into a definite noun phrase.
Overlevende comes from the verb å overleve = to survive.
It is originally a participle-like form, similar to surviving in English, but in Norwegian it is also very commonly used like a noun:
en overlevende = a survivor
den overlevende = the survivor
So in this sentence, overlevende is functioning as a noun meaning survivor, even though its form is closely connected to the verb å overleve.