na-adjective, noun
ruined; spoiled; coming to nothing
Describes a state where something is completely ruined, spoiled, or rendered useless, often after effort or expectation. Used as a noun or adjectival noun.
雨でピクニックが形無しになった。
The picnic was ruined by the rain.
計画が形無しだ。
The plan has come to nothing.
noun, na-adjective
complete loss of face
Specifically refers to a total loss of face, dignity, or reputation. Often used in social contexts where one's standing is destroyed.
彼は公の場で失敗して形無しになった。
He suffered a complete loss of face after failing in public.
台無し also means 'ruined' or 'spoiled', but is more common and often used for things being wasted or messed up, while 形無し can carry a stronger nuance of losing shape/form or face.
Compound of 形 (かた, 'shape, form') and 無し (なし, 'without'). Literally 'formless', it came to mean something that has lost its proper shape or state, hence 'ruined' or 'disgraced'.