Skeletons in the cupboard/closet

embarrassing or damaging information about you that you would like to remain secret

many politicians live with the fear that past misdemeanours will be exposed; that someone will reveal the skeletons in their cupboard.

The phrase was first used in the early 1800s. The first reference in print appears to be in a piece by William Hendry Stowell, in the UK monthly periodical The Eclectic Review, 1816. The 'skeleton' in this case was disease, infectious or hereditary.