How were plantation owners affected by the Great Depression in America?

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,

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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.