唇chún亡wáng齿chǐ寒hán

Literal: with the lips gone, the teeth feel cold
Figurative: When one falls, the other is endangered; two neighbors share a common fate and depend on each other.

Where does 唇亡齿寒 come from?

During the Spring and Autumn period, the state of Jin wished to attack the state of Guo and asked the state of Yu for passage through its territory in exchange for gifts. The minister Gong Zhiqi warned the Duke of Yu: Guo and Yu shield each other like lips and teeth; "if the lips are gone, the teeth feel cold." Should Jin destroy Guo, Yu would fall next. Blinded by the gifts, the duke ignored him and granted passage. Jin conquered Guo and, on its way back, wiped out Yu as well.

Source (出处): 《左传》

How is 唇亡齿寒 used? Two examples

两liǎng家jiā公gōng司sī供gōng应yìng链liàn紧jǐn密mì相xiāng连lián，唇chún亡wáng齿chǐ寒hán，一yī家jiā倒dǎo了le另lìng一yī家jiā也yě难nán撑chēng。
The two companies' supply chains are tightly linked; their fates are bound together—if one collapses, the other won't hold up either.
邻lín国guó之zhī间jiān唇chún亡wáng齿chǐ寒hán，他tā国guó遭zāo难nàn时shí不bù该gāi袖xiù手shǒu旁páng观guān。
Neighboring countries share a common fate; when another suffers disaster, one should not stand idly by.

In Wanyu, all 400 chengyu have audio on every sentence, and you can save them to your decks and review them with spaced repetition. Free.