Place dead corn stalks in your compost bin or compost pile. The stalks will biodegrade with other compost ingredients to form a nutrient-rich garden additive.
Call your town's Department of Public Works to ask about disposal of corn stalks, if you do not have a home compost pile. Towns have different policies for proper disposal of garden clippings like corn. The City of Milwaukee requires residents to self-compost the corn or take it to a Milwaukee "Self Help Center." Only in fall do they collect garden clippings curbside, as part of leaf collection. The City of Waterville, Ohio collects corn stalks year-round as part of a weekly yard waste collection.
Dispose of the dried corn stalks using your town's preferred procedure. There may be fees associated with disposal. The City of Waterville, as of 2011, assesses a fee of $2.25 for each yard waste bag you throw out.