I mention about this in bug https://www.w3.org/Bugs/Public/show_bug.cgi?id=27022#c1.

Now only Firefox support URLSearchParams so examples will presents result only for this browser. There still is space for corect this browser or change something in URL spec.

By spec "query object" can be set from null to URLSearchParams when "set the input" is used. In some case null will stay, but in IDL I don't see nullable type for .searchParams. 

Simple case:

var someURL = new URL("aaa:bbb");

If I understand all algos, then this step from "set the input":
  5. If url is non-null and its relative flag is set, run these substeps
will be never executed and "query object" stay with null (initial value) and someURL.searchParams should return null.

Next case is important for HTML, how treat this:

<a>
<a href="parserReturnError">

a.searchParams should return null or URLSearchParams object with empty list?
Now HTML denided this wrong (https://www.w3.org/Bugs/Public/show_bug.cgi?id=27047) but before correct HTML, URL spec should be correct.

What can I add is that Firefox always create URLSearchParams.

<a id="a1"></a>
<a id="a2" href></a>
<a id="a3" href="abc:def"></a>

<script>

 var a1 = document.getElementById("a1");
 var a2 = document.getElementById("a2"); // the same as href="" and probably use base URL
 var a3 = document.getElementById("a3");

 var a4 = new URL("abc:def");

 document.write(a1.searchParams.append + "<br><br>"); // function append() { [native code] }

 document.write(a2.searchParams.append + "<br><br>"); // function append() { [native code] }

 document.write(a3.searchParams.append + "<br><br>"); // function append() { [native code] }

 document.write(a4.searchParams.append + "<br><br>"); // function append() { [native code] }

</script>

This is still fresh and can be easy correct (by URL spec or Firefox) but its important what behaviour is excepted.