Silver stain is a hazardous waste material and as such it cannot be poured down the drain. Instead it must be disposed of following recommended protocols.

The recommended method of disposing silver stain is to put the staining solution in a disposable plastic or hazardous waste container under the hood.  Leave it there untouched for one to two days till the silver metal precipitates from the solution. After the silver has precipitated, the aqueous waste can be easily decanted from the silver and disposed of separately. 

Disposing both the aqueous and solid silver stain waste must comply with local and state rules and regulations.