We typically use the word "plantation" to refer to the large farms that dominated the Southern economy during the time when slavery was still legal in the US. This was, of course, long before the Great Depression. I will assume that you are using "plantation" to mean "farm."
Farmers were, like everyone else, hit very hard by the Great Depression. It may well have been worse for farmers because they were already suffering economically. Farm incomes had been dropping since the end of WWI so farmers were already doing badly at the start of the Depression. When the Depression came, demand for their crops dropped even further, both in the US and abroad. This meant that many farmers lost their ability to make a living. Many of them stopped being able to pay back loans and, therefore, lost their land to the banks. As the link below tells us,
Between 1929 and 1932 approximately four hundred thousand farms were lost through foreclosure.
Farmers, then, were hit hard by the drastic decline in demand for their crops that came about as a result of the Great Depression.