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Related to sponge on: sponge off
sponge on (someone or something)
To take advantage of someone else's generosity, charity, or hospitality in order to obtain something, typically money or food, as a handout. My brother's been sponging on my parents ever since he dropped out of college. I hated being on welfare—even though I really needed it, I always felt like I was sponging on the government
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
Also, sponge off. Impose on another's hospitality or generosity, as in He's been sponging on relatives for the past year. This expression uses sponge in the sense of "to soak up something." [Late 1600s]
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.