Part a: as it is used in paragraph 1, the phrase "closing the slightest avenue" means:
a. to close or block off a street
b. putting an end to slavery once and for all
c. to prevent slaves from using existing routes of escape
d. to make slave-owners more aware of the efforts to free slaves :

B. Putting an end to slavery once and for all.

Explanation:

The text that the question is based off is the memoir "The Narrative of the Life of Frederick Douglass", Chapter XI  Part I.

"I would allow myself to suffer under the greatest imputations which evil-minded men might suggest, rather than exculpate myself, and thereby run the hazard of closing the slightest avenue by which a brother slave might clear himself of the chains and fetters of slavery."

The phrase "closing the slightest avenue" in relation to the sentence it is on could refer more to the ending of slavery and that too, not temporary but more on the permanent scale. Considering he was talking about being a "hazard [for] a brother slave" clearing himself, the narrator could be referring to the idea of putting an end to slavery altogether.

man vs. nature - first choice