Is there a word for "Someone who/Something that caches"?

Solution 1:

In computer science, the word is cache. The same word is used for the collection of items, as the routines responsible for managing them.

Solution 2:

"Cache" is borrowed from French, and should mean a store with an implied meaning of hidden but easily accessible to the "right people". Because of that I do not like using "cacher", which is the infinitive of the French verb.

The uncommonly used French word would be a "cacheur".

The word that actually had the meaning, and has become specialised in its own ways, is cashier.

Other words from the same Old French roots are "stash", almost synonymous with cache, and "stasher". I think I prefer "stasher".