Why do these snippets of JavaScript behave differently even though they both encounter an error?

Actually, if you read the error message properly, case 1 and case 2 throw different errors.

Case a.x.y:

Cannot set property ‘y’ of undefined

Case a.x.y.z:

Cannot read property ‘y’ of undefined

I guess it’s best to describe it by step-by-step execution in easy English.

Case 1

// 1. Declare variable `a`
// 2. Define variable `a` as {}
var a = {}

// 1. Declare variable `b`
// 2. Define variable `b` as {}
var b = {}

try {

  /**
   *  1. Read `a`, gets {}
   *  2. Read `a.x`, gets undefined
   *  3. Read `b`, gets {}
   *  4. Set `b.z` to 1, returns 1
   *  5. Set `a.x.y` to return value of `b.z = 1`
   *  6. Throws "Cannot **set** property 'y' of undefined"
   */
  a.x.y = b.z = 1
  
} catch(e){
  console.error(e.message)
} finally {
  console.log(b.z)
}

Case 2

// 1. Declare variable `a`
// 2. Define variable `a` as {}
var a = {}

// 1. Declare variable `b`
// 2. Define variable `b` as {}
var b = {}

try {

  /**
   *  1. Read `a`, gets {}
   *  2. Read `a.x`, gets undefined
   *  3. Read `a.x.y`, throws "Cannot **read** property 'y' of undefined".
   */
  a.x.y.z = b.z = 1
  
} catch(e){
  console.error(e.message)
} finally {
  console.log(b.z)
}

In comments, Solomon Tam found this ECMA documentation about assignment operation.

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