I wonder if Ophelia actually foresaw Emilia running away, and the letter was meant to deal with that eventuality. Considering Ophelia's words to Emilia, before she died, that Emilia should live, date, and marry smoothly, this could be Ophelia trying to make sure it actually happens. At the same time, Ophelia and Emilia's relationship obviously wasn't simple, so I bet arranging the letter wasn't out of pure, innocent goodwill either.