Alternatively, you could send your ship on the other side of ourGalaxy... after all, I'm sure there are a lot of areas that are not explored at the time of TNG, so this leaves room for lots of unexplored places. For instance, they could end up in the Gamma Quadrant, in an area the Dominion has not invaded(yet ?) , or a Borg-free sector in the Delta Quadrant (hey, the poor guys meeting the Kazons), or on the opposite side of the Alpha Quadrant (far beyond the future Cardassian Union's outer reaches).
For the matter of losing hope to come home... the way I understand it, wormholes can indeed send people anywhere (and anywhen), so if they came through a wormhole, they could hope to find another one to get back.
Just my 0.02€
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett