**Yes**, the lone player gets the cards.

The [Official FAQ at catan.com][1] answers this directly.

> **Resource Cards** - In case not enough Resource Cards of a certain type are available, does a player get nothing even if he is the only one to receive this resource?
>
>No. In this case, he receives all available Resource Cards of this type.


  [1]: http://www.catan.com/faq/4621-resource-cards-case-not-enough-resource-cards-certain-type-are-available-does-player-get