Slip-ups: Inverted sentences and concord

We have looked at the slip-ups that occur in sentences as a result of the subjects of those sentences not agreeing with their verbs in terms of number.

For instance, we now know that the sentence:

There is a woman and her son living in that house

is incorrect because the subject of the sentence: a woman and her son, does not agree with the verb is.

This is because the subject, a woman and her son, is plural and must agree with a plural verb, not the singular verb is.

We have learnt that a subject must agree with its verb, even if the normal sentence order (subject before verb) is inverted, such that we have the verb before the subject, as in:

Here comes the man and his wife.

This sentence is, of course, incorrect because the subject, the man and his wife, is plural and must agree with a plural verb.

If we go by the normal order of sentences, the sentence above should be:

A man and his wife come here.

Therefore, even if the order is inverted, we must still make the subject and the verb agree, as in:

Here come the man and his wife.

But note that it is also correct to write or say:

Here comes a man with his wife.

Can you explain why this is correct?