But I have read in a book, in a different context, when Bromonium ion executes NGP, the bond with which it donates lone-pair is weaker than the bond with the carbon atom to which it was attached. In that case, Bromine shouldn't migrate, should it?
I think experimental examples will clear up the confusion. But I couldn't find any.
I am in agreement with this. However, that does not describe the example given. In acid, loss of water can generate a hypothetical carbocation adjacent to a tertiary bromide. Donation of electrons from the bromine will give the indicated bromonium ion. The "bonds" of the bromonium ion will not be equal. Tertiary carbons are more electron rich resulting in a weaker C-Br and more easily broken bond. If it were the stronger bond, then it would not break and no migration would have occurred. (This similar to tertiary bonds being weaker and react faster under SN1 conditions.)
This is the essence of the similar epoxide opening question. I was arguing that if the reaction were driven by nucleophilic attack, then attack should occur on the least substituted carbon. If it does not occur there, then bond breakage must be playing a greater role in the reaction. Again, when isobutylene oxide were reacted, apparently bond breakage must have become the greater factor.
I view these two examples as similar in nature. I don't necessarily consider chloride to be a strong driving force for attack per se. The charges are balanced, but one also needs to consider bond breakage as part of an analysis. Here I like using examples to help me judge how great one factor might be compared with another.
If you are reading between the lines, then you might consider that in SN1 reactions bond cleavage occurs before bond formation and in SN2 reactions attack occurs before blond cleavage, but in actual examples, reactions occur between these two extremes. Our job is to recognize how that might be true. Just an opinion.