You can bind to variables with NULL values, and on update and insert queries, the corresponding field will be updated to NULL no matter what bind string type you associated it with. But, for parameters meant for the WHERE clause (ie where field = ?), the query will have no effect and produce no results.
When comparing a value against NULL, the MYSQL syntax is either "value IS NULL" or "value IS NOT NULL". So, you can't pass in something like "WHERE (value = ?)" and expect this to work using a null value parameter.
Instead, you can do something like this in your WHERE clause:
"WHERE (IF(ISNULL(?), field1 is null, field1 = ?))"
Then, pass in the value you want to test twice:
bind_param('ss', $value1, $value1);
