Multicellular organisms as DNA banks
This paper seems relevant. I just found it and don't have access, so I haven't read it. It does seem to suggest that there is evidence for eukaryotic genes being taken up by a prokaryote.

I would imagine this is rare, though. Eukaryotic cells don't tend to just spew their genetic material everywhere. Most death pathways involve breaking down any genetic material in the cell, I believe.