Friar Lawrence gave the letter to Friar John to deliver to Romeo. While he was on his way, he stopped at a house to visit the sick. Since the authorities suspected that the house might have the plague, Friar John and all those inside were put under quarantine until it could be determined if they carried the disease or not. They refused to take the letter to Romeo on Friar John's behalf because the letter might have carried the contagion, and so it was never delivered. Not knowing the gravity of the situation, once he was released, Friar John gave the letter back to Friar Lawrence saying that he wasn't able to deliver it. At first, the Friar started to panic, but then he decided that he would simply go to the tomb, get an awakening Juliet, and then hide her in his cell till he could get word to Romeo. Plan B didn't work out either because Friar Lawrence didn't know that Romeo had charged his friend Balthasar with bringing him news from Verona to keep him on top of things. Balthasar got to Romeo with the sad news that Juliet was dead and buried in the Capulet vault before Friar Lawrence could let him know that it was all a hoax. As a result, Romeo bought poison and killed himself next to a "dead" Juliet. She woke up immediately afterwards and refused to leave with the Friar. OUt of self-preservation, Friar Lawrence left her alone in the tomb and she killed herself with Romeo's dagger.
Romeo did not receive Friar Lawrence's letter because Friar John, who was sent with the letter, was quarentined while visiting the sick and was unable to make it all the way to Mantua (Act 5, scene 2). Friar Lawrence did not realize that Romeo knew nothing of the plan until Friar John returns, and thus has to go to meet Juliet in the tomb himself, so that someone is here when she wakes up. This unfortunate occurance is another example of fate's work within the tragedy.