Green’s Dictionary of Slang

1. a cowardly boxer, one who cannot take the punches [he ‘folds up’, thus fold v.].

1938

D. Runyon ‘The Big Umbrella’ in Runyon on Broadway (1954) 557: If Jonas is not a big umbrella he will be fighting somebody who can really fight.

2. cowardice.

1938

D. Runyon ‘The Big Umbrella’ in Runyon on Broadway (1954) 562: ‘You can boff this big ape [...] unless,’ she says, ‘there is even more umbrella in you than I ever suspect.’.

3. (US) police protection, obtained through bribery [it keeps one from being ‘rained on’ – see rain on under rain v.].

1968

‘Sl. of Watts’ in Current Sl. III:2.