Conditionally check whether a Matrix is empty when searching on a particular column. Can be used with a Playa relationship field.

EE: Matrix: If no results on search

{if '{parent:total_rows search:child="not IS_EMPTY"}' == 0}
    ...
{/if}

You can use the search:col_name= parameter in combination with :total_rows:

Where 'parent' is the matrix field name and 'child' is the matrix column name.

Here's an example of how it might look using the :total_rows and search in an EE conditional

{if "{matrix_field:total_rows search:column_name=''search term here"}

    {matrix_field search:column_name=''search term here"}
        <p>{col_names} … etc.</p>
    {/matrix_field}

{if:else}

    {other_custom_field}

{/if}