I'm guessing you already know about Pat's death being recorded in Cook County and the undertaker's burial record from Philadelphia. Both can be seen at beta.familysearch.org
I would imagine his death was reported in the Philadelphia newspapers.
I don't know if you have his parents or not, but Patrick and Denis are with his parents Denis and Mary and sister Mary in the 1870 census of Philadelphia under the spelling of Killon. They also appear in the 1880 census of Philadelphia, however, they are misindexed under the name Hillen.
Under Philadelphia deaths are Dennis, who died in 1884, and Mary, who died in 1887. Both are buried in Cathedral Cemetery. The same undertaker was used as for Patrick.
Under Minnesota deaths is a Dennis J. Killen who died in 1892 at age 26.
Under Minnesota births is a Marcus born to Patrick Killen and Jessie Clarabel Simsen on July 19, 1890.
The Historical Society of Pennsylvania has a large collection of Philadelphia records. You might also try the Philadelphia Archdiocesan Historical Research Center: http://www.pahrc.net/http://www.pahrc.net/. They might be able to help you find more on the family including christenings for Patrick and Dennis.
As for finding anything on what happened to Jessie or Marcus it may have to wait until more records are online. I could not find a Marcus or Mark with a mother Jessie and born in July 1890 anywhere in the country in the 1900 census. It is possible Marcus did not live or he took his step father's first name as well.
One possibility would be if Patrick or Dennis Jr left an estate. If Dennis died without any children his estate would have gone to the next of kin which may have been Patrick's children. Patrick's estate may have been settled in Philadelphia or Chicago. You might also check the orphans court records for Philadelphia. Deeds are also a possibility. The elder Dennis and Mary's estates may not have been settled right away. It's a long shot but you never know.