Kerry Mergen, a contract egg farmer near Albany, Minn., got word on a Wednesday the chickens in his barn would be euthanized. A crew showed up the next morning and started gassing the birds with carbon dioxide. The sudden drop in demand for food at restaurants, school cafeterias and caterers shut down by the pandemic has ripped through farming. Milk has been dumped, eggs smashed and ripe lettuce plowed under. Now, farms are killing animals sooner than planned. Mergen said he initially couldn’t believe it when a field manager from Daybreak Foods, the Lake Mills, Wis.-based firm that owned and...