For weird, have them get a message from StarFleet to patrol into Klingon Space, (maximum priority command etc...) Once inside Klingon space, they are no longer able to communicate with Fed Space, (but may not realize this for a while under comm silence), and discover no Klingon signals either.
Have them meet another curious ship from another culture which doesn't know what's going on either. For extra weird, have that ship vaguely resemble the ship they are in, but with identifiable differences...
Other ways it could turn out:
Actually, it was all the result of a botched experiment in a SuperCloaking device that temporarily shifted the Klingon Empire out of time for two weeks, four days, and seventeen minutes from mark...
And now they're back! With several curious Romulan, Fed, and other ships hovering over their capital planet...