WJYS seems to be happy as it is. It has a niche market, it took over the infomercial / home shopping from WEHS, Channel 60, (Now TeleFutura) and it was a shopping channel before. Then it took over the niche of WCFC Channel 38, (Now Pax), and it's even picked up some leftover ethnic shows from WCIU's subchannel.
It's owned by Oxford Media Group
but I can't tell exactly from the website what they are about, except for marketing. Which may be it.
WJYS seems to be doing OK picking up everyone else's leftovers. Add to the fact that WJYS is no longer a rimshot as it is off the Willis (Sears) Tower now.
When WEHS (Channel 60) went for sale, that was the last time anyone in Chicago tried for a duopoly seriously. Tribune and Disney seriously looked at it, but the USA Broadcasting, which owned it cut a nationwide group deal with Univision, and that left Disney out.
I remember when FOX bought WPWR for 450 million that was a record, at the time, for a UHF station. (Back in the analog days)
The Chicago market is saturated, the most likely sale of a TV station will come if Tribune can't come out of its bankruptcy intact and has to sell off its TV stations one by one.