It's no surprise that Dunn would go unclaimed since he has close to $20 million to go on his contract through the end of next year, but he's hitting very well lately and potentially could help someone if Chicago finds a trade partner.
Dunn's overall numbers (26 home runs, 69 RBI, .227 average, .797 OPS) are decent but he has been hitting better in recent days, with a .297 batting average since the break and .391 (9 for 23) in August.
The Rangers and Orioles are two teams that might consider at least looking at DH, though the White Sox would presumably have to pay down significant dollars. Texas also has a greater need for a right-handed bat, not a lefty like Dunn.
The Rangers were the team that claimed Dunn's teammate Alex Rios as they look to shore up right field following the Biogenesis suspension for star Nelson Cruz. The chances for a deal there weren't being portrayed as necessarily likely. Rios would be a good fit in Texas, though, and the Rangers showed they are willing to take his contract, which pays him $12 million this year, $12.5 million next year and has a buyout and an escalator in the event of a trade.