Yes, the family settled in the township of Wesley, Will Co., Illinois.(Today, that's part of Wilmington, I think.)William and Sarah Beard are buried in the Wesley Cemetary.
In rechecking my files, though, I saw that I did have a spouse filled in for John L. Beard after all--May Taylor--so there could be descendants.Unfortunately, I don't have a date for the marriage and I'm not positive he stayed in Will Co.
Hope this helps some.If I come across any other notes on the sons, I'll be sure to let you know. I'm glad your 25-year-old mystery has been at least partially solved.