In the first place, it's a clause, not a sentence.
Also, it is not even syntactically correct.
A valid clause might be
had a stray dog not given them away, ...
a use of the subjunctive, equivalent to
if a stray dog had not given them away, ...
had a stray dog not have given them away.
what's the grammatical name n function of the sentence?
14 answers
Noun clause
What sorts function
It is an adverbial clause
Adverbial clause
Adverbial clause
Adverbial clause
Noun clause
Adverbial clause of time
Adverbial Clause
Adjectival clause
Adverbial clause
Complex Sentence
Noun phrase
1 answer