To Dangle
To Hang Down, To Drip
intransitive verb, ichidan verb
If 垂らす is "to dangle something" then 垂れる is to dangle or to drip on its own. So you can use 垂れる to describe your dog's floppy ears hanging down or your ice cream’s melty goodness dripping away. You know this because it's rare (れる) to witness the moment something starts dangling or dripping down.
Sometimes, 垂れる can also take a direct object in specific expressions, like 説教を垂れる (to give a preachy lecture), こうべを垂れる (to bow one's head in humility), or the crude slang クソを垂れる (to drop a load).
The reading is the same as 垂らす.
フタがちゃんと閉まっていなかったみたいで、横からソースが垂れている。
It seems that the lid wasn't properly closed, so there's sauce leaking from one side.
昨夜ジャグチが壊れて、水がポタポタ垂れる音が気になってほとんど寝られなかった。
Last night the faucet broke, and the sound of dripping water bothered me so much I hardly got any sleep.
ジャズの尻尾は飼い主がいない間ずっと垂れ下がっていたが、次郎の車が聞こえた途端、ぴんとはね上がり、激しく振り始めた。
Although Jazz's tail had been drooping the entire time his owner was out, the moment he heard Jiro's car, it sprang straight up and started wagging furiously.