It is up to the DM
"Willing" and "unwilling" are not game terms and are not defined anywhere in the rules and thus we are stuck with generic definitions.
- not willing; reluctant; loath; averse:
- opposed; offering resistance; stubborn or obstinate; refractory:
"Willing" at least is pretty clearly a choice, you are mentally choosing to consent to something. "Unwilling" is much less clear.
Unwilling has at least two opposed ways to interpret it
As per the above definition, "unwilling" can mean, in broad strokes, "the absence of willingness" (thus an unconscious person would be by default unwilling) or it can mean "opposed" (which requires a conscious decision and thus an unconscious creature would not be considered unwilling).
Depending on what definition you are using either
you must choose to be (un)willing and thus you can be in a neutral state where you are neither.
you are always one or the other thus not choosing to be willing means you are automatically unwilling.
Both are valid definitions.
DM decides ambiguities
The term is ambiguous, in other words, and the person who decides that at your table will be the DM. There is simply no way to magic away the ambiguity of the English language in this case.
At my table
For what it is worth, in my games, I treat all characters as being unwilling unless they are explicitly willing and have had no issues, confusion, or complaints.