‘Unwillingly’ because it is, of course, the character not the actress who is unwilling.
Typically the character may be: a prison inmate; arriving at a concentration camp; a wartime collaborator; other sorts of punishment haircut; and other unwanted – including both the spiteful and the accidental – haircuts..
When it comes to portraying a character having their head shaved on-screen, it’s hard to fake – though it has been done as with Cameron Diaz in My Sister’s Keeper and Patricia Arquette in Human Nature – so the role usually comes with a heavy price.
Sometimes it’s for that extra bit of authenticity; sometimes it’s for the money; sometimes it’s for the publicity that might revive a flagging career or kick-start a new one. I don’t understand why most of the actresses who have appeared bald in movies agreed to have their heads shaved: why they would agree to it being filmed and how they could have the confidence that they could remain in character throughout the process is beyond me.