Announcing an unspoken prayer request leaves the rest of the group no choice but to speculate as to what could possibly be the matter. If a girl has requested “an unspoken” you may assume she needs prayer for her Woman Bits. If a guy has requested “an unspoken” you may assume he needs prayer for his chronic masturbating.
The unspoken prayer request is meant to offset gossip via prayer request (as previously discussed here) but manages to spark gossip anyway. Unspoken-prayer-request gossip is even juicier than normal prayer-request gossip thanks to its speculative nature. If you have been entrenched in Christian culture for awhile then you know what will be assumed when you announce your unspoken need and often you will just let it go un-prayed for rather than invite any dirty presumptions.