Zugzwang
Etymology
From German Zugzwang, from Zug (“move,” as in a chess move) plus Zwang (“compulsion, force”) — so “compulsion to move.” It began as a chess term for a position where any move damages your own game, and spread to describe forced no-win choices in general.
noun · /TSOOK-tsvang/
A situation in which you are forced to act even though every available move makes things worse.
What it names
The particular trap of compulsory action — you would gladly stand still, but the rules require a move, and there is no good one.
Example
By election night the mayor was in zugzwang: raise taxes and lose the base, cut services and lose everyone else.
Related idea
A dilemma offers bad options; zugzwang is worse — you would happily do nothing, but the rules force you to move and every move hurts.