The two shadow-piercing combinators have been removed, as stated in https://www.chromestatus.com/features/6750456638341120
So, what's the substitute for achieving the same thing? Or has this shadow-piercing feature been completely abandoned?
The two shadow-piercing combinators have been removed, as stated in https://www.chromestatus.com/features/6750456638341120
So, what's the substitute for achieving the same thing? Or has this shadow-piercing feature been completely abandoned?
::shadow and /deep/ were removed for breaking encapsulation.
The substitutes are:
:host-context. Read here: http://www.html5rocks.com/en/tutorials/webcomponents/shadowdom-201/As of Polymer 2:
::shadow (shadow-piercing selectors) - there is no direct substitute. Instead a custom CSS properties has to be used. Polymer 2: Custom CSS Properties
/deep/ - there is some sort of replacement by defining :host > * { ... } (applies a ruleset to all of the top-level children in the host's shadow tree, which doesn't conflict with the rule in the main document). 
For more detailed information check Polymer 2 Upgrade Notes
At the time of writing you can try ::part and ::theme with Chrome 73 and above:
https://www.chromestatus.com/feature/5763933658939392
<submit-form>
  #shadow-root
  <x-form exportparts="some-input, some-box">
    #shadow-root
    <x-bar exportparts="some-input, some-box">
      #shadow-root
      <x-foo part="some-input, some-box"></x-foo>
    </x-bar>
  </x-form>
</submit-form>
<x-form></x-form>
<x-bar></x-bar>
You can style all the inputs with:
:root::part(some-input) { ... }
There is the full documentation how it works:
https://github.com/fergald/docs/blob/master/explainers/css-shadow-parts-1.md
This somehow can solve your problem, but I still miss the days how I styled embedded tweets with ::shadow.
"::v-deep" is working for me. For example:
    .menu {
        // stuff
    }
    /deep/.sub-menu {     // override submenu
        .sub-menu__mini {
                //stuff
            }
            a, a:hover {
                //stuff
            }
        }
    }
becomes:
    .menu {
        // stuff
    }
    ::v-deep .sub-menu {     // override submenu
        .sub-menu__mini {
                //stuff
            }
            a, a:hover {
                //stuff
            }
        }
    }