If you think your tires are "slipping," you are almost certainly mistaken. When a motorcycle's tires actually lose traction in a corner, the bike almost invariably lowsides, bang, right then and there.
Unless you're leaned way over, and are dragging parts hard enough to lever the rear wheel off of the ground, or unless you've just hit a gravel patch, the tires aren't likely to be slipping: what you're feeling is probably just the 250's frame and suspension flexing and/or the tires "walking" sideways a bit across irregularities in the pavement. All motorcycles do this to some extent, and it's generally nothing to worry about (huge chuckholes, frost heaves, or nasty tar snakes being obvious exceptions.)
While it's impossible to make one statement that can cover all the variables in these situations, you are usually much better off to hold your line through a corner rather than run off of the outside. While you might go down if you attempt to hold your line, you will almost certainly go down if you run off the pavement. Sliding down the road from a lowside will probably damage both yourself and your bike, but not as badly as would laminating yourself to a common roadside object such as a tree, rock, cow, or armco barrier.
If it's possible for you to attend a track school such as Reggie Pridmore's CLASS or Keith Code's California Superbike School (they travel around the country), you should. Getting out on a track with fresh tires will allow you to learn exactly what you and your bike can (and cannot) do in a reasonably safe place, where you don't have to worry about oncoming traffic or gravel. Most riders who haven't done any track time really have no idea of just how hard a motorcycle can corner (very) before the tires actually do lose traction.