seep out
1. Of a liquid, gel, paste, etc., to leak or flow out of some crack, breach, or flaw in something. I realized there was a fire downstairs when I noticed smoke seeping into our bedroom. I made sure to make the container airtight so no moisture seeps in.
2. To become known to those from whom (something) was supposed to remain secret or classified. The senator always held himself up as a beacon of moral standards, but as rumors and details of his infidelities and substances abuses seeped out, he eventually became a pariah among his constituents. News of the merger seeped out months before the two companies made a formal announcement about it.