Slight correction: all tags will get a closing tag if it’s missing; it’s just less likely to be where you want on tags that “require” an end tag than those where it’s explicitly optional. Remember that HTML defines an exhaustive parser: all inputs produce a defined tree. “Invalid HTML” means a nonconforming document, but it doesn’t actually change anything; it’s just a way of making you feel guilty, or pointing out a place where it’s very likely you made a mistake or might make a mistake in further modifying the document.

If you have something like this:

    <div>
        <h1>A
        <p>B
            <img>
        <p>C
        <h2>D
        <p>E
    </div>

… it’ll parse to this:

    <div>
        <h1>A
        <p>B
            <img>
        </p><p>C
        </p></h1><h2>D
        <p>E
    </p></h2></div>

See, the headings did get closed eventually, even without their proper closing tags; it just wasn’t where you wanted, either time. (The paragraphs, on the other hand, probably ended where you expected.)

Of your example, I think you typed it incorrectly in a couple of places. Here’s what I think you meant to express (plus a third one to make things clearer with the second having a bad trailing slash):

    <ul>
        <li>first
        <li/>second
        <li>third
    </ul>

… and here’s what that is precisely equivalent to:

    <ul>
        <li>first
        </li><li>second
        </li><li>third
    </li></ul>