A mutation in the second base of the codon UGA (which is a stop codon) would change it into a different codon. The possible mutations for UGA in the second base could result in UAA (also a stop codon) or UGU/UGC (coding for cysteine), among others.
If the mutation turned UGA into either UAA or UAG, it would still result in a stop signal, potentially not affecting the overall length of the protein significantly.
However, if the mutated codon changed to UGU or UGC, the stop signal would be lost, and the protein translation would continue beyond that point, which would normally lead to an unusually long protein because it would keep translating until it encounters another stop codon.
Given this information, the best choice based on the mutation in the second base of UGA would be:
The resulting protein would most likely be unusually long.