user25684: There are three possible outcomes of a game of chess: white wins, black wins, or the players draw.
Typically, we consider a win better than a draw, so when we say "white can force a draw" from a given position, usually we mean "white can force a draw or better (a win)".  For the purposes of this question, consider the three possible results of a game as entirely separate possibilities.  For example, in this question, a position is given where

white cannot force a win nor a draw (remember, exactly a draw),
black cannot force a win, nor a draw, nor a loss, but
white can force a loss.

(This is interesting because "neither player can force a win nor [exactly] a draw".)  Is something more extreme possible?  Is there a position where

white cannot force a win, nor a draw, nor a loss, and
black cannot force a win, nor a draw, nor a loss?

For example, this would mean that if white attempts to force a white loss, then they cannot because black can force that either white wins or the players draw (but without actually being able to choose which).

user4418: 
Is there a position where white cannot force a win, nor a draw, nor a loss, and
black cannot force a win, nor a draw, nor a loss?

Of course there is. It's a position we are all very familiar with. Here it is:
[fen ""]


user8860: Such a position must be a draw with best play.
Here's one where either player can make a winning threat
that can only be parried by giving checkmate:
[Title "Neither player can force an exact outcome"]
[FEN "2n4k/2P3pP/6P1/8/8/6p1/2p3Pp/2N4K w - - 0 0"]

1. Nd3 Nd6 2. Ne5?!?

Best play is for White and Black to keep moving their Knights
back to c1 and c8 respectively.  But either player can prevent a
drawn outcome
by threatening mate in at most two moves with Ne5 or ...Ne4,
forcing the opponent to either mate in 1 (by promoting to Q or R)
or get mated.

25684: <p>There are three possible outcomes of a game of chess: white wins, black wins, or the players draw.</p>
<p>Typically, we consider a win better than a draw, so when we say &quot;white can force a draw&quot; from a given position, usually we mean &quot;white can force a draw <em>or better</em> (a win)&quot;.  For the purposes of this question, consider the three possible results of a game as entirely separate possibilities.  For example, in <a href="https://chess.stackexchange.com/questions/40623/position-where-neither-player-can-force-a-win-and-neither-player-can-force-a-dra">this question</a>, a position is given where</p>
<ul>
<li>white cannot force a win nor a draw (remember, <em>exactly</em> a draw),</li>
<li>black cannot force a win, nor a draw, nor a loss, but</li>
<li>white can force a loss.</li>
</ul>
<p>(This is interesting because &quot;neither player can force a win nor [exactly] a draw&quot;.)  Is something more extreme possible?  Is there a position where</p>
<ul>
<li>white cannot force a win, nor a draw, nor a loss, and</li>
<li>black cannot force a win, nor a draw, nor a loss?</li>
</ul>
<p>For example, this would mean that if white attempts to force a white loss, then they cannot because black can force that either white wins or the players draw (but without actually being able to choose which).</p>
 4418: <blockquote>
<p>Is there a position where white cannot force a win, nor a draw, nor a loss, and
black cannot force a win, nor a draw, nor a loss?</p>
</blockquote>
<p>Of course there is. It's a position we are all very familiar with. Here it is:</p>
<pre><code>[fen &quot;&quot;]
</code></pre>
 8860: <p>Such a position must be a draw with best play.
Here's one where either player can make a winning threat
that can only be parried by giving checkmate:</p>
<pre><code>[Title &quot;Neither player can force an exact outcome&quot;]
[FEN &quot;2n4k/2P3pP/6P1/8/8/6p1/2p3Pp/2N4K w - - 0 0&quot;]

1. Nd3 Nd6 2. Ne5?!?
</code></pre>
<p>Best play is for White and Black to keep moving their Knights
back to c1 and c8 respectively.  But either player can prevent a
drawn outcome
by threatening mate in at most two moves with Ne5 or ...Ne4,
forcing the opponent to either mate in 1 (by promoting to Q or R)
or get mated.</p>
