Stories don't get used up no matter how much you tell them.

Literal

Stories [topic-は] tell [even if-ても] at-all don't-decrease.

A proverbial observation: unlike physical goods, stories aren't depleted by sharing. 語る is a slightly more literary synonym of 話す, carrying a nuance of narration rather than casual chat. 全然~ない ('not at all') reinforces that no amount of telling has any effect.