index.js

var stream = require("stream")

getSourceStreamThatThrowsError().
  on("error", console.error.bind(null, "source stream")).
  pipe(getDestinationStreamThatThrowsError()).
    on("error", console.error.bind(null, "dest stream"))

function getSourceStreamThatThrowsError() {
  var rs = new stream.Readable

  var readCount = 0
  rs._read = function () {
    readCount++

    this.push(String(readCount))

    if (readCount == 3) {
      this.push(null)
      this.emit("error", new Error("read failed"))
    }
  }
  return rs
}

function getDestinationStreamThatThrowsError() {
  var fs = new stream.Writable

  var writtenCount = 0
  fs._write = function (chunk, enc, next) {
    writtenCount++

    if (writtenCount == 2) {
      this.emit("error", new Error("write failed"))
      this.end()
    }

    next()
  }

  return fs
}

$ node ./
source stream [Error: read failed]
dest stream [Error: write failed]

:(