A castaway is a person who is cast adrift or ashore. While the situation usually happens after a shipwreck

Shipwreck

A shipwreck is what remains of a ship that has wrecked, either sunk or beached. Whatever the cause, a sunken ship or a wrecked ship is a physical example of the event: this explains why the two concepts are often overlapping in English....

, some people voluntarily stay behind on a deserted island, either to evade their captors

Kidnapping

In criminal law, kidnapping is the taking away or transportation of a person against that person's will, usually to hold the person in false imprisonment, a confinement without legal authority...

 or the world in general. Alternatively, a person or item can be cast away, meaning rejected or discarded. Note that when a person was left ashore as punishment, usually the term maroon

Marooning

Marooning is the intentional leaving of someone in a remote area, such as an uninhabited island. The word appears in writing in approximately 1709, and is derived from the term maroon, a word for a fugitive slave, which could be a corruption of Spanish cimarrón, meaning a household animal who has...

(or marooned) was used.

The provisions and resources available to castaways may allow them to live on the island until other people arrive to take them off the island.