Is it customary to express heat loss as a negative number?
Your assumptions are correct, and from the wording of the question, the "correct" answer doesn't make sense, unless like you said, the object gained heat, which is possible; people have negative profits all the time. Sign conventions are not flawed in chemistry, but you just have to be careful when wording a question. To answer the title of your question, yes it is not only customary, it is necessary to express heat loss as a negative number, but the question still has to be phrased correctly--using the term "lost" serves as a negation in this use of language, the same way the unary operator in -1 serves as negation for a number. If heat loss were not expressed negatively, it wouldn't make sense because the system of an exothermic reaction must lose energy for its surroundings to gain it.