==> "The entire lot of scofflaws deserves to be rounded up and punished."
That could be either singular or plural depending on context. Does 'lot' has a specific meaning or is it a quantifier? That question can only be answered in context. If 'lot' is the subject, (i.e. the scofflaws have been grouped together into lots), then it's singular and would call for a singular verb. In that case 'of scofflaws' is a prepositional phrase. If you remove the prepositional phrase, the sentence becomes: "The entire lot deserves to be rounded up and punished." You're talking about a specific lot.
However, the subject could also be 'scofflaws', which is plural, and therefore calls for a plural verb. In that case, 'entire lot of' is a quantifier and if removed, the sentence becomes: "The scofflaws deserve to be rounded up and punished." Either could be correct, depending on context.
One test that you can do is substitute "many" or "all" for the phrase that may be a quantifier. For example, is the sentence, "All the scofflaws deserve to be rounded up and punished." semantically equivalent to "The entire lot of scofflaws deserves to be rounded up and punished."? If All = The entire lot, then scofflaws is the subject. If not, as would be the case if they were grouped into lots, then lot is the subject.
In any event, the rule is the same: Singular subjects require singular verbs and plural subjects require plural verbs. Find the subject, determine its number, use the corresponding number for the verb.
What's difficult in sentences that begin with 'there is' and 'there are', is that identifying the subject can be tricky because the sentence is not in subject-verb order. The subject is behind the verb.
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