We do not normally use not/n't or never with
another negative word.
I didn't see anyone. NOT I didn't see no one.
That will never happen. NOT That
won't never happen.
We've hardly started. NOT We
haven't hardly started.
In non-standard English, a double
negative means the same as a single negative. I didn't see
no one. (non-standard)
(= I didn't see anyone./I saw no one.)
In standard English a double negative has a
different meaning.
I didn't see no one. I saw one of my friends. (= I saw someone.)
We can't
do nothing. (= We
must do something.)
NOTE
We
sometimes use a negative after I wouldn't
be surprised if/It wouldn't surprise me if...
I wouldn't be surprised if it rained/if it didn't rain.
The speaker expects that it will rain.