go begging

go begging and go a-begging(to be unclaimed, unsold, unwanted or unused; as if an object were begging for an owner or a user) — лежать без дела; валяться без дела; пропадать; ~ бесхозный

Example 1: There is still food left. A whole lobster is going begging. Please eat some more.

Example 2: There are many excellent books in the library just going begging because people don’t know they are there. — ...замечательные книги лежат без дела, пылятся в библиотеке потому что о них никто не знает. (NTC’S American IDIOMS Dictionary)

Example 3: I'll have the last cake if it's going begging.

see
[up for grabs]
[gather dust]
валяться [без дела] (2)