Last night I drove by the illuminated sign of a national chain. Two consecutive letters in the sign were burned out. “Hmm,” I thought to myself, “If one new letter were added to the sign, it could be used for a sandwich shop.” Later, I drove past the sign in the other direction. On the other side of the sign two consecutive letters were burned out, both different from the burned-out letters on the side I originally saw. “Hmm,” I thought to myself, “If new one letter were added to the sign, it could be used for a … Gilbert & Sullivan theater.”
What national chain was the sign for?
life as a puzzle 
I guess this was tougher (or less interesting) than I thought. I’ll add more information by saying that “sandwich shop” could be replaced by “Southern sandwich shop” and “Gilbert & Sullivan theater” could be replaced by “theater mounting a production of ‘The Mikado’.”
Jeffrey Harris posted a clever alternate solution — better than the intended one — that I’ll reveal later.
I can only come up with “whulyh” for the chain, because “vwlyh” would work for the theater part but I am stuck on the sandwich shop bit of it so maybe I am way off. Spoilers are encoded with a Caesar cipher with a shift of 7.
Another interesting approach, but it’s not related to the sign I saw.
Answer: Pep Boys (pO boys and pEep bo)