CSS position: sticky and overflow

Not able to find the solution for this. Basically, what I am trying to achieve is to have an element with the position: sticky appear with a scrollbar if there is more content then the browser height.

I don't want to use position: fixed as it will add additional pain in the neck.

Here is the example of how I would expect it to work:

.placeholder {
  height: 200vh;
  width: 50%;
  float: right;
}

.child {
  position: fixed;
  top: 0;
  bottom: 0;
  height: 100%;
  overflow-y: auto;
}

<div class="parent">
  <div class="placeholder"></div>
  <div class="child">
    some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br /> some long text
    <br />

  </div>
</div>

Fiddle 1

Here is example with the position: sticky where the overflow doesn't do anything:

.placeholder {
  height: 200vh;
  width: 50%;
  float: right;
}

.child {
  position: sticky;
  top: 0;
  bottom: 0;
  height: 100%;
  overflow-y: auto;
}

<div class="parent">
  <div class="placeholder"></div>
  <div class="child">
    some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  some long text <br />
  
  </div>  
</div>

Fiddle 2

Any explanation / solution appreciated.

Make sure to use Firefox when testing