I don't see any serious problem here. You always have some amount of shearing and most of the time a large number of sheared fragments have length around 15-20 kb. you have a log ladder so the band you see is not 10kb. it is > 15kb.

may be a plasmid DNA like the classic 2µm yeast plasmid

Microbe often contain cryptic plasmid. The plasmid can be replicated within the host cell. You can check the band and construct shuttle vector.

Agree with Herve, It could be 2micron Plasmid. Try a yeast plasmid miniprep kit to extract plasmid and see if you still could get the same size band.

David is perfectly right. Yo do not see entire chromosomes or very-high molecular weight DNA unless you are extremely careful and use special procedures for DNA preparation (such as embedding the cells in agarose blocks etc.). All other procedures will break the DNA into pieces. Imagine a glass rod that is 1 mm wide but several meters long.  Can you handle it without destroying it? Yes you can but you have to be extra careful!

Thanks everyone for the answers.

David, is there any particular reason to think that the band near the well is just staining material besides the fact that genomic DNA should be sheared down in a conventional purification? I've never observed stuck ethidium bromide like this in any other gels and samples. Bands near the wells like that only happen in genomic samples. The top ladder band is 10 kb linear, so the lower genomic band is maybe 15 - 20 kb, and the top band should be something much higher.

Thank you.

DNA that does not migrate or migrates very little could also be bound to protein. A proteinase K digest allows you to decide if this is the case. 

Best wishes

Juergen