Do you mean the Mr. Tuffy kind of tire liner? When I first bought my bike I used those in my tires. They wore a hole in the inner tube, and the tire went flat one morning about a mile from work (fortunately).
If you know
that you will be riding through a region with a lot of puncture problems, then I suggest that you bring thorn-resistant inner tubes, and install them just before entering the area. These inner tubes are as heavy as a tire, so riding with them will sap a good 2mph off of your speed.
A tire sealant in an inner tube, like Slime, will leave a tube virtually unpatchable.
I rode the Seattle-to-Portland group ride (200mi) with Continental Town and Country tires, and nothing punctured those. Other people got lots of flats, while I kept riding along. You might also consider Schwalbe Marathon Plus (built-in liner) and Marathon XR (Aramid fiber tire carcass).
Some of the extra-security tires weigh more, but they don't make your speed suffer. After my Continental SportContact tires got nailed by glass, I put on Schwalbe Marathon XR which weigh twice as much, and my distance speed doesn't suffer. Yeah, my sprinting speed is down, but I'm only going after the groceries.