Bedsheet stained with William Seward’s blood after the failed assassination attempt on his life.
Image Source: Seward House Museum
Blood stained sheet
The History Behind Lincoln's Assassination
Bedsheet stained with William Seward’s blood after the failed assassination attempt on his life.
Image Source: Seward House Museum
LincolnConspirators.com 
Judging from the material texture and the similarity of the rip to the slice in Seward’s jaw beside his chin that he was photographed with as an old man, it appears this was actually the BANDAGE wound around his fractured jaw from the carriage accident to cushion his skin from the metal brace supporting his face.